ENVIRONMENTAL ENGINEERING-1Published by : LAXMI PUBLICATIONS (P) LTD. 22, Golden House, Daryaganj, New Delhi-110002. Phones , | 011-28262368 * | 011-23 26 23.70 011-23 25 2572 011-23 26 2279 Faxes : Branches : 129/1, Ird Main Road, IX Cross, Chamrajpet, Bangalore (Phone : 080-26 61 15 61) 26, Damodaran Street. T. Nagar, Chennai (Phone : 044-24 34 47 26) St. Benedict’s Road, Cochin (Phone : 0484-239 70 04) Pan Bazar, Rani Bari, Guwahati (Phones : 0361-254 36 69, 251 38 81) 4-2-453, Ist Floor, Ramkote, Hyderabad (Phone : 040-24 75 02 47) Adda Tanda Chowk, N.D. 365, Jalandhar City (Phone : 0181-222 12 72) 106/A, Ist Floor, S.N. Banerjee Road, Kolkata (Phones : 033-22 27 37 73, 22 27 52 47) 18, Madan Mohan Malviya Marg, Lucknow (Phone : 0522-220 95 78) 142-C, Victor House, Ground Floor, N.M. Joshi Marg, Lower Parel (W), Mumbai (Phones : 022-24 91 54 15, 24 92 78 69) Radha Govind Street, Tharpagna, Ranchi (Phone : 0651-230 77 64) EMAIL : colaxmi@hotmail.com WEBSITE : www.laxmipublications.com SECOND EDITION : SEPT. 1995 REPRINT : JULY 1998 REPRINT : AUG. 1999 REPRINT : AUG. 2001 REPRINT : AUG. 2002 REPRINT : AUG. 2003 REPRINT : SEPT. 2004 REPRINT : JUNE 2005 ISBN : 81-7008-092-4 EWS-0617-135-WATER SUPPLY ENGG ©1996 = B.C. PUNMIA, ASHOK K. JAIN, ARUN K. JAIN All Rights Reserved by the Authors. This book, or parts thereof, may not be reproduced in any form or translated in any other language, without the written permission of the Authors. Price : Rs. 135.00 Only. C—10774/05/06 DTP Composed by : Arihant Consultants, Jodhpur. Printed at : Mehra Offset Press, DelhiCONTENTS CHAPTER 1. WATER SYSTEMS LL 12. 13. 14. Introduction Historical Development Sources _of Water Water Supply Systems CHAPTER 2. HYDROLOGY 21. 22. 23. 24. 25. 26. 27 28. The Water Cycle Precipitation Measurement of Rainfall Computation of Average Rainfall over a Basin Evaporation and Transpiration Run-off Computation of Run-off SS aT R ff Runoff Flood Discharge CHAPTER 3, SURFACE SOURCES 31. Storage Reservoirs 3.2. Investigations for Reservoir Planning 33. — Selection of Site for a Reservoir 34. St ity and Yield 35. Dams 3.6. Intakes CHAPTER 4. GROUND WATER : WELLS 41. Introduction 42. of Aquifers 43. Storage Coefficient 44, Well Hy tics 45. Determination of Aquifer Constant T 4.6. Characteristic Well Losses : Specific Capacity of Well 47. Interference Among Wells oa Ne BBRBSCUESSBEESSEEEREEEE ©) Fully Penetrating Artesian-gravity Well Partially Penetrating Artesian Well Spherical Flow in a Well ‘Tube Wells Methods for Drilling Tube Wells ‘Well Shrouding and Well Development Open Wells Yield of an Open Well Selection of Suitable Site for a Tube Well Section of a Tube Well Unsteady Flow Other Sources of Underground Water Radial Collector Wells CHAPTER 5. WATER DEMAND AND QUANTITY BER BEBBE Introduction Design Period Population Forecast Factors Affectin; ulation Growth Determination of ulation for Inter-censal and_Post-censal Years Water Demand Factors ing Rate of Demand Variations in R D CHAPTER 6. QUALITY OF WATER 61 62 63. 64, 65. 66. 67. 68. 69. 6.10, 611. Introduction Common Impuritiesin Water and their Effect BBE Bgeee 107 BBE EERE BEREGi) CHAPTER 7. UNIT OPERATIONS 7.1. Introduction 72. Important Unit Operations 123. Gas Transfer 74. — Ton Transfer 75. Solute Stabilization 7.6. Solids Transfer 7.7, Water Treatment Processes CHAPTER 8 SCREENING AND AERATION 8.1. Screening 8.2. Coarse Screens or Bar Screens 8.3. Fine Screens 8.4. Micro-strainers 8.5. Aeration 8.6. Types of Aerators 8.7. Factors Governing Aeration or Gas Transfer 8.8. Design of Gravity Aerators 8.9. Design of Fixed Spray Acrators 8.10. Limitations of Aeration CHAPTER 9. SEDIMENTATION 91. Introduction 9.2. Types of Settlings 9.3, Settling of Discrete Particles 9.4. Types of Sedimentation Tanks 9.5. Horizontal Flow Sedimentation Tank 9.6. Size-weight Composition and Removal 9.7. Maximum Velocity to Prevent Bed Uplift or Scour 98. Design Elements 9.9. Settling Tank Efficiency 9.10. Details of Plain Sedimentation Tanks 9.11. Sedimentation with Coagulation. : Clarification 9.12. Common Coagulants 9.13. Methods of Feeding Coagulants 213 214 216 217 217 218 225 228 231 232 BEES SRRBIRB9.14. 9.15. 9.16. 9.17. 9.18. 9.19. 9.20. 9.21. Gai) Mixing Devices Flocculation Clarification - Sludge Blanket Tanks or Solid Contact Clarifiers The Pulsator Clarifier Shallow Depth Sedimentation : Tube Settler INustrative Examples Design Examples CHAPTER 10. FILTRATION 10.1. 10.2. 10.3. 10.4, 105. 10.6. 10.7. 108. 10.9. 10.10. 10.11. 10.12, 10.13. 10.14, 10.15. 10.16. 10.17. 10.18. 10.19, 10.20. 10.21. Introduction Theory of Filtration Classification of Filters. Filter Media Slow Sand Filters Rapid Sand Filter : Gravity Type Working and Washing of Rapid Sand Filters Loss of Head and Negative Head Filter Troubles Performance of Rapid Sand Filters Comparison of Slow Sand and Rapid Sand Filters Filtration Hydraulics : Carmen-Kozney Equation : Rose Equation Flow through Expanded Beds Pressure Filters Double Filtration : Roughing Filter Dual Media and Mixed Media Filters Upfiow Filters Biflow Filters Micro-strainers Diatomite Filters 274 277 282 285 287 29 298 311 311 312 312 314 320 329 330 331 333 335 342, 345 353 355 355 357 359 359(uti) CHAPTER 11. DISINFECTION 11.1. Introduction = 363 11.2. Methods of Disinfection ~ 364 11.3. Minor Methods of Disinfection o 365 11.4. Chlorination ~~ 366 11.5. Forms of Application of Chlorine 368 11.6. Application of Chiorine «372 11.7, Forms of Chlorination «= 374 11.8. Tests for Free and Combined Chlorine “~ 379 11.9. Factors Affecting Bactericidal Efficiency of Chlorine ~ 381 11.10. Kinetics of Chemical Disinfection 385 11.11. Iodine Treatment - 390 11.12. Bromine Treatment = 391 11.13. Ozone Treatment (ozonation) ~ 391 CHAPTER 12. WATER SOFTENING 12.1. Introduction = 394 12.2. Type of Hardness and Methods of their Removal 395 12.3. Lime-soda Process 396 12.4. Lime-soda Softening Plant 402 12.5. Water Softening Accelerator 404 12.6. Zeolite Process 405 12.7. Advantages and Disadvantages of Lime Soda and Zeolite Process 407 12.8. Demineralisation or Deionisation Process 408 CHAPTER 13. MISCELLANEOUS TREATMENT METHODS 13.1. Removal of Iron and Manganese 410 13.2. Colour Odour and Taste Removal ww. 413 13.3. Activated Carbon Treatment ww «414 13.4. Use of Copper Sulphate 417 13.5. Fluoridation - 417 13.6. Defluoridatioa. = 418 13.7. Desalination - = «49Gav) CHAPTER 14. PUMPS AND PUMPING 14.1. Necessity of Pumping «427 14.2. Types of Pumps and their Choice «427 143. Displacement Pumps 430 14.4. Centrifugal Pumps 433 145. Comparsion of Reciprocating and Centrifugal Pumps aw 435 146. Jet Pump a 436 14.7. Air Lift Pumps a 437 148. Well Pumps o 438 149. Centrigual Pump Installation «440 14.10. Characteristics of Centrifugal Pump ae 441 14.11. Multiple Pump Systems we 442 14.12. Variable Speed Operation we 44d 14.13. Suction Lift Limitations : Cavitation 445 14.14. System Head Curve wa 446 14.15. Operating Point or Operating Range of a Pump ow 448 14.16. Selection of Pumping Units w 449 14.17. Power Requirements of Pumps ~ 450 14.18. Economical Diameter of Pumping Mains wen 452 CHAPTER 15, CONVEYANCE OF WATER 15.1, Introduction -~ 473 152. Pipes a 414 153. Cast Iron Pipes a 474 15.4. Wrought Iron and Galvanised Iron Pipes = 479 155. Steel Pipes 480 15.6. Cement Concrete Pipes «480 15.7. Asbestos Cement Pipes 482 15.8. Copper and Lead Pipes 483 15.9. Wood-stave Pipes 483 15.10. Plastic Pipes 484 15.11. Stresses in Pipes 485 15.12. Corrosion in Pipes 49115.13. 15.14, @) Pipe Appertenances Head Loss through Pipes CHAPTER 16. DISTRIBUTION OF WATER 16.1. 16.2. 163. 16.4. 165. 16.6. 16.7. 16.8. 16.9. 16.10. 16.11. 16.12. 16.13. Introduction Methods of Distribution Pressure in Distribution Mains Systems of Water Supply Storage and Distribution Reservoirs ‘Types of Storage and Distribution Reservoirs Capacity of Distribution Reservoir Pipe Hydraulics Pipes in Series and Parallel Layout of Distribution System Design of Distribution System Analysis of Pressure in Distribution System Hardy Cross Method CHAPTER 17. WATER SUPPLY FOR BUILDINGS 17.1 Materials for Service Pipes 17.2. Service Connection 17.3. Size of Service Pipes 17.4. Water Meters 17.5. Valves 17.6. Loss of Head through Pipes and Pipe Fittings APPENDIX INDEX 494 499 504 505 552 555 558 562Water Systems 1.1. INTRODUCTION The five essential requirements for human existence are : (i) air (ii) water (ii) food (jv) heat and (v) light. Contamination of these elements may cause serious health hazards not only to man but also to ‘animal and plant life. Environmental Engineering deals with all these essential elements. The use of water by man, plants and animals is universal. Without it, there can be no life. Every living thing requires water. Man and animals not only consume water, but they also consume vegetation for their food. Vegetation, in turn, cannot grow without water. Growth of vegetation also depends upon bacterial action, while bacteria need water in order to thrive. The bacterial action can convert vegetable matter into productive soil. New plants, which grow in this soil, grow by sucking nutrients through their roots in the form of solution in water. Thus an ecological chain is maintained. Water maintains an ecological balance — balance in the relationship between living things and environment in which they live. The use of water is increasing rapidly with our growing popula- tion. Already there are acute shortages of both surface and under ground waters in many parts of the country. Careless pollution and contamination of the streams, lakes, reservoirs, wells and other under ground sources has greatly impaired the quality of available water. This pollution results because of improper disposal of waster water —both domestic as well as industrial. Organised community life require twin services of water supply and sewage disposal. Good sanitation cannot be maintained without adequate water supply system. Without ®2 WATER SUPPLY ENGINEERING Proper disposal, the wastes of a community can create intolerable nuisance, spread diseases and create other health hazards. The planning, designing, financing and operation of water and waste water systems are complex undertakings, and they require a high degree of skill and judgement. The work of construction and maintenance of water supply and waste water disposal systems is generally undertaken by Government agencies - mostly through Public Health Engineering or Environmental Engineering Departments consisting of Civil Engineers. 1.2. HISTORICAL DEVELOPMENT Man’s search for pure water began is prehistoric times. The story of water supply begins with the growth of ancient capital cities, or religious and trade centres. In olden days, most of community settlements throughout the World were made near springs, lakes and rivers from where the water supply for drinking and irrigation purposes was obtained. Rig Veda (4000 years B.C) makes a mention of digging of wells. Similarly, Ramayana, Mahabhartha and Puranas make mention of wells as the principal source of water supply. These wells were mostly of shallow depth, dug near river banks. Water was lifted from the -wells through indegenous methods. However, no water treatment or distribution works existed. Apart from India (Bharat), other major civilisations of the World, such as Greece, Egypt, Assyria etc. used wells for their settlements which were located slightly away from springs, lakes and rivers. Joseph’s well at Cairo is one of the oldest deep wells excavated in rock to a depth of about 300 feet. These wells, however, caused water supply problems during periods of drought. It became necessary, therefore, to store water. Cisterns were constructed for collecting rain water while reser- voirs were constructed to store water from streams and rivers during monsoon period. The stored water was conveyed to towns through masonry conduits and aqueducts. The earlier examples are the aqueducts built by Appius Claudius in about 312 B.C. for water supply to Rome. Lyons in Paris, Metz in Germany and Segovia and Serille in Spain built similar aqueducts and syphons for water supply used for drinking, bathing and other purposes. Sextus Julius Frontinus, Water Commissioner of Rome (A.D. 97)-reported the existence of nine aqueducts supplying water to Rome and- varying in Jength from 10 to over 50 miles and in cross-section from 7 to over 50 sq. ft., with an estimated aggregate capacity of 84 mgd. The great sewer, known as the cloaca maxima and constructed to drain the Roman Forum, is still in service. There was practically no improvement in water supply systems in the middle ages. The earlier water supply structures got destroyed with the fall of Rome. In the ninth century, few important waterWATER SYSTEMS 3 supply structures were constructed by the Moors in Spain. In the twelfth century, small aqueduct was constructed in Paris. In London, spring water was brought by means of lead pipes and masonry conduits in the thirteenth century. In Germany, water works were constructed in 1412 and pumps were introduced in 1527 in Hanover. Franciscan monk constructed aqueduct of Zempola in Mexico in ihe middle of 16th century. In 1582, a pump was erected on the old London bridge for the supply of water from the Thames. The water was conveyed through lead pipes. In Paris, pumps operated by water power were erected in 1608. Pumps operating from steam were in- troduced in the 18th century in London and Paris. In the United States, spring water was conveyed by gravity to Boston in 1652. Pumps etc, were introduced at Bethlehem in 1754. However, purposeful quality control of water supply is quite recent in origin. The scientific discoveries and engineering inventions of the eighteenth and nineteeth centuries created centralised industries to which people flocked for employment. This caused serious water supply and waste disposal problems in the industrial towns. No great schemes of water supply were started until the Industrial Revolution had well passed its first half century. The development of the large impounding reservoir was largely due to the necessity of feeding canals constructed during the first phase of the Industrial Revolution. The first water filter was constructed in 1804 by John Gibb at Paisley in Scotland. It was a slow sand filter and worked in conjunction with a settling basin and roughening filter. Next successful filters were constructed in 1827 by Robert Thom at Greenock. In 1829, James Simpson built sizable filters for the Chelsea Water Company to improve its supply from the Thames river. By 1870, the mechanical filter of the pressure type began to be employed, the earliest being the Halliday filters installed at Crewe (1888), Bridlington and elsewhere. In 1894 pre-filters were successfully built. In the first decade of 20th century, mechanical pressure filters were introduced, Hastings being an early pioneer with Canndy filters built in 1900. In India, Calcutta was the first city where a modern water supply system was constructed in 1870. The technique of clarification and filtration soon grew. By 1939, mechanically-sludged sedimentation tanks were in general use. The micro-strainer, for the removal of plankton from the impounded water was developed by Boucher, and was introduced by Glenfield and Kennedy in 1945. Coagulation of water with sulphate of alumina began experimentally in 1827, but was adapted practically only in 1881 to treat Bolton’s water supply. Activated silica was introduced by Bayliss in U.S.A. during 1937. The first permanent use of chlorination originated under the direction of Sir Alexander Houston at Lincoln4 WATER SUPPLY ENGINEERING in 1905. In 1917, Paterson Engineerihg Company insialled the first gaseous chlorinator at the Rye Common Works. Super-chlorination and dechlorination was first applied in 1922 at the Deptford works of the Metropolitan Water Board. The art of softening water was also first developed in Great Britain. The first municipal softener was constructed by Plumstead in 1854. Development of the softener took a novel turn in 1912 by the construction, at the Hooten works of the West Cheshire Water Board, of a base exchange softener. Since India was under British occupation, water supply schemes in India were undertaken practically about the same time as in England, though with a slower rate. In 1870, a water supply system was const- Tucted at Calcutta. Till Independence, only few cities had protected water supply systems. 1.3. SOURCES OF WATER The following are common sources of water (Rain water (ii) Surface water (#i) Ground water — (iv) Water obtained from reclamation. 1, Rain Water (b) FROM PREPARED CATCHMENTS FIG. 1.1. DIRECT: COLLECTION OF RAIN WATERWATER SYSTEMS 5 (a) From roofs of houses and dwellings ; Water is stored in smail underground tank or cistern, for small individual supplies (Fig. 1.1 a). (b) From prepared catchments : The surface of catchments is made impervious by suitable lining material, and suitable slope is given so that water is stored in moderate size reservoirs. This water is used for communal supplies, mostly for drinking purposes. 2. Surface Water INTAKE TOWER TO PURIFICATION ‘WORKS: (c) WATER FROM RESERVOIR STORAGE FIG. 1.2. SOURCES OF SURFACE WATERaa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.8 WATER SUPPLY ENGINEERING ‘1.4. WATER SUPPLY SYSTEMS The primary objective of water treatment for public supply is to take water from the best available source and to ‘subject is to processing which will ensure water of good physical quality, free from unpleasant taste or odour and containing nothing which might be detrimental to health. The treatment of water to improve its quality involves additions to, substractions from, or chemical changes in the raw water. Municipal water systems consist of the following units. 1, Collection works 2. Transmission works 3. Purification works and 4. Distribution works. , These systems have been shown diagrammatically in Fig. 1.4. DISTRIBUTION SYSTEM FIG. 1.4. WATER SUPPLY SYSTEMS L. Collection Works Collection works are meant for the development of surface water or ground water resources. For major cities, or where water requirements are large, water is collected from a surface source— mostly a river or stream. If the river is perennial, a direct intake structure can be built on the river bank. If, however, river is not perennial, a dam is built across the river so that water is storedaa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.12 WATER SUPPLY ENGINEERING (2) Interflow or sub-surface run off A portion of precipitation infiltrates into surface soil and, depending upon the geology of the basin, runs as sub-surface run- off and reaches the streams and rivers. (3) Ground water flow or base flow It is that portion of precipitation, which after infiltration, per- colates down and joins the ground water reservoir which is ultimately connected to the ocean. Thus, the hydrologic cycle may be expressed by the following simplified equation. Precipitation = Evaporation + Run off @= € + provided adjustment is made for the moisture held in storage at the beginning and at the end of the period. 2.2, PRECIPITATION To the hydrologist, precipitation is the general term for all forms of moisture emanating from the clouds and falling to the ground. The foliowing are the essential requirements for precipitation to occur : 1. Some mechanism is required to cool the air sufficiently to cause condensation and droplet growth. 2. Condensation nuclii are also necessary for formation of droplets. They are usually present in the atmosphere in adequate quantities. 3. Large scale cooling is essential for significant amount of precipitation. This is achieved by lifting of air, Thus a meteorological ‘phenomenon of lifting of air masses is essential to result precipitation. Types of Precipitation Precipitation is often classified according to the factors respon- sible for lifting. Broadly speaking, there are four types of precipitation. (1) Cyclonic precipitation. (2) Convective precipitation (3) Orographic precipitation (4) Precipitation due to turbulent ascent. 1. Cyclonic Precipitation Cyclonic precipitation results from lifting of air masses con- verging into low pressure area or cyclone. The cyclonic precipitation may be divided into (a) frontal precipitation, and (b) non-frontal precipitation.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.16 WATER SUPPLY ENGINEERING ‘CLOCK DRIVEN RECORD DRUM FIG. 2.3. WEIGHING BUCKET RAIN GAUGE 3. Tipping Bucket Type Rain-gauge The tipping bucket type rain-gauge consists of a 30 cm diameter sharp edge receiver. At the end of the receiver is provided a funnel. A pair of buckets are pivoted under the funnel in such a way that when one bucket receives 0.25 mm (0.01 inch) of precipitation it tips, discharging its contents into a reservoir bringing the other bucket under the funnel. Tipping of the bucket completes an electric circuit 1 30cm—4 FIG. 2.4. TIPPING BUCKET TYPE RAIN-GAUGEaa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.18 WATER SUPPLY ENGINEERING Thus, if Pi, P, Ps... ... » Py etc, arf the precipitation or rainfall values measured at m gauge stations, we have eit Pt... + Py EP - - (2-1) Pow 2. Thiessen Polygon Method The arithmetic average method is the most approximate method since rainfall varies.in intensity and duration from place to place. Hence the rainfall recorded by each rain-gauge station should be “weighted according to the area it is assumed to represent. Thiessen polygon method is a more common method of weighting the rain-gauge observations according to the area. Thiessen polygon method is also called weighted mean method and is more accurate than the arithmetic average method. FIG. 2.6. THIESSEN POLYGON METHOD Procedure 1. Join the adjacent rain-gauge stations A, B, C, D etc., by straight lines. 2. Construct the perpendicular bisectors of each of these lines. 3. A Thiessen network is thus constructed. The polygon formed by the perpendicular bisectors around a station encloses an area which is everywhere closer to that station than to any other station. Find the area of each of these polygons shown hatched in Fig. 2.6. 4. Multiply the area of each Thiessen polygon by the rain-gauge * value of the enclosed station. 5. Find the total area (2A) of the basin. 6. Compute the average precipitation or rainfall from the equationHYDROLOGY 19 Poy = At Pit AoPa + agian tafe Ex?) (2.2) 3. Isohyetal Method The basic assumption in the Thiessen polygon method is that a rain-gauge station best represents the area which is close to it. However, this may not always be valid, specially when the rainfall is controlled by topography or results from intense convection. The isohyetal method is the most elaborate and accurate in such conditions. An isohyet is a line, on a rainfall map of the basin, joining places of equal rainfall readings. An isohyet map showing contours of equal rainfall presents a more accurate picture of the. rainfall distribution over the basin. FIG. 2.7, ISOHYETAL METHOD Procedure 1. From the rainfall values recorded at various rain-gauge sta- tions, prepare the isohyetal map for the storm causing the rainfall over the area. 2. Measure the areas enclosed between successive isohyets with the help of a planimeter. 3. Multiply each of these areas by the average rainfall between the isohyets. 4, The average rainfall is then computed from the expression Sa (2 +h) Pay = DISCHARGE Q (CUMECS) 1957 58 59 «60S! 62 63 64 «65 66 —> TIME (YEARS) FIG 33, FLOOD HYDROGRAPH OF INFLOW38 WATER SUPPLY ENGINEERING > MASS INFLOW (!000ha-m) 1957 58 59 60 61 62 63 64 65 66 —™ TIME (YEARS) FIG. 3.4. MASS INFLOW CURVE shows accumulated inflow. If there is no inflow during certain period, the mass curve will be horizontal during that period. The mass curve will rise very sharply during the period of high flood. Thus the steepness of the mass curve shows the rate of inflow at that time interval. The hollows on the mass curve show relatively dry periods. Demand curve. A demand curve (Fig. 3.5) is a plot between accumulated demand with time. The demand curve representing a uniform rate of demand is a straight line having the slope equal to the demand rate. A demand curve may be curved also indicating variable rate of demand. ACCUMULATED DEMAND ACCUMULATED DEMAND (he-m) TIME 'YEAR (a) tb) FIG. 3.5. DEMAND CURVEaa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.40 WATER SUPPLY ENGINEERING It should be noted that the vertical distance between successive tangents represent water wasted over the spillway. The spillway must have sufficient capacity to discharge this flood volume. Corresponding to the numerical figures indicated in Fig. 3.6, we observe that (1) The required reservoir capacity is 2100 ha-m. (2) Assuming the reservoir to be full at Aj, it is depleted to (2100 — 800)= 1300 ha-m at D,, and is again full at By. (3) Assuming the reservoir to be full at A), it is empty at Dy, and is again full at B, (4) The reservoir is full between B, and A2, and the quantity of spill is 800 ha-m. DETERMINATION OF SAFE YIELD FROM A RESERVOIR OF A GIVEN CAPACITY The following is the procedure of determining the safe yield from a reservoir of a given storage capacity, with the help of a mass inflow curve : > MASS INFLOW.(100 ha-m) a 3 w = u ¢ 4 bel YEAR -> SAFE YIELD 60 6I 62 6 64 65 —> TIME (YEARS) FIG. 3.7. DETERMINATION OF YIELD FROM RESERVOIR OF SPECIFIED CAPACITYSURFACE SOURCES 4 (1) Prepare the mass inflow curve. On the same diagram, draw straight lines, from a common origin, representing demands at various rates, say varying from 0 to 5000 ha-m per year. (2) From the apices 4,,-A2, As, etc. of the mass curve, draw tangents in such a way that their maximum departure from the mass curve does not exceed the specified reservoir capacity. Thus, in Fig. 3.7, the ordinates E,D,, E2 D2, E;Ds, etc. are all equal to the reservoir capacity (say 1500 ha-m). (3) Measure the slopes of each of these tangents. The slopes indicate the yield which can be attained in each year from the reservoir of given capacity. The slope of the flattest demand line is the firm eld, {ANALYTICAL METHOD FOR COMPUTING RESERVOIR CAPACITY ‘When the demand is variable, it is preferable to carry out the computations for storage in a tabular form. Example 3.2 gives the procedure for computations. In this method, the variations in precipitation and evaporation data can be easily accounted for. As- suming that the reservoir is full at the beginning of a dry period, the maximum amount of water S that must be withdrawn from storage to maintain a given average draft or demand D equals to the maximum cumulative difference between the draft (or demand) D and adjusted inflow J in a given dry period, or S = maximum value of 2(D—-J/) - COMPENSATION WATER AND RESIDUAL FLOW RULES When a dam is constructed across a river or a stream so that storage reservoir is formed behind it, the flow to the downstream side is very much affected. Most of the wells may be situated on the river banks downstream, and hence if a minimum flow is not maintained to the downstream side, these wells will dry up. Com- pensation water is the flow that must be discharged below a storage reservoir to compensate the riparian interests for the water taken away to supply. While calculating the reservoir capacity, the com- pensation water should be kept in mind. Each country has its own rules of compensation water ; such rules are known as _ residual flow rules. It is often realistic to assume that compensation water need not be greater than the flow which is normally exceeded for 90% of the time. Example 3.1. A distribution reservoir is to be constructed for supplying water to a city. Water is pumped from wells to the distribution reservoir at a uniform rate of 25 cumecs. The estimated hourly re- quirements for the maximum day are tabulated below. Estimate the capacity of the distribution reservoir.42 WATER SUPPLY ENGINEERING Time_{hours) Demand (million litres Solution : The average pumping rate is determined by the total demand by 24. Hence average pumping rate = =7 million litres/fnour. TABLE 3.2aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.44 WATER SUPPLY ENGINEERING SPZBL TIN TIN UN ES eres ove ILE 8861 tL oss - svol — evel + orozt + SLES + 20°69 + 98SE - 80% — 9606 — orl = 8b - as - 00 oo oo wy 8@ on 6 102 - § o= ) 8 1024£ 109 — 9 102=¢ 702 = (uoy) 1 woyuy patsnipy (9) fF 109 x9 = (ue-oy) uopondioadgy wo £ POOKoE= (ueoy) 7 uoposodoay re ATSVLSURFACE SOURCES 45 Column 8 gives the precipitaion in hectare metres, falling over the reservoir area. Since 30% of the precipitation is already reaching and has been included in the inflow (column 2), only 70% of the precipitation has been included in the computation. Thus the precipita- tion P is calculated from the relation — Reservoir area x column (4) P 700 «0.7 — 200 x column (4) = 100 x 0.7 = 3.5 xcolumn (4) hectare-metres. Column 9 gives the adjusted inflow (I) computed from the relation 1 =column (2)— column (6)- column (7) + column (8) Column (10) gives the water required from storage (ie. S) and is computed from the following relation : S=D-I or Column (10)= column (5)— column (9) In the above relation, only positive values are to be included. When column (9) (ie. adjusted inflow) is more than column (5), zero values are to be written in column (10) indicating that no water is required. from the storage since demand is much less than the adjusted inflow. The required storage is the sum of the monthly increments of demand in excess of stream flow. The required storage capacity in this case works out to be 281.64 ha-m. Example 3.3. Table 3.5 gives the details about the average seasonal discharges of a river for 12 years. Determine the storage capacity required to maintain a flow of 475 cumecs throughout the year. - TABLE 3.5 16th June to Ist Oct. to Ist April to 30th Sept. (cumecs) | 31st March (cumecs) | 15th June (cumecs) 1050 3000 3500 2000 1200 1400 3600 3000 700 800 2400 320046 WATER SUPPLY ENGINEERING Solution : Let the periods from 16th June to 30th Sept, Ist Oct. to 31st March and Ist April to 15th June be designated as M, W and S. The data for preparing mass inflow curve are tabulated in Table 3.6. The mass inflow curve is shown in Fig. 3.8. TABLE 3.6 DATA FOR MASS-INFLOW CURVE Cumulative volume (million ha-mm) 0.9707 1.4424 1.4752 4.2486 4.6417 4.6680 7.9037 8.4855 85446 10.3936 10.6295 10.7083, 11.8177 12.3681 12.4108, 13.7051 14.3341 14.3998, 17.7279 18.0424 18.0949 20.8673, 21.1032 21.1820 21.8291 22.1593, 22.1921 22.9317 23.1204 23.1729 25.3917 25.8949 25.9737 28.9320 29.3723 29.4248 ASK SE VEE weE ek SE vSX SE SF 1X EE eTaa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.48 WATER SUPPLY ENGINEERING of 1.5 m ha-m in 1 year. The ordinates Oy, Oy, ......Os indicate the deficiencies during the dry periods, assuming that the reservoir was full at the beginning of the period. The maximum of these ordinates (ce. Os = 1.6 m ha-m) gives the desired reservoir capacity. 29 J |_RESERVOR DRAWN DOWN i DEPLETION OF STORAGE 4 REPLENISHMENT 28 —rClor storase re ie 27 » o Led saan ca os | RES.EMPT RES.FULL. Lg b x a RESERVOIR FULL x & MASS INFLOW (MILLION HECTARE METRE) n 1967 1968 1970 1971 I TIME FIG. 3.9. DETERMINATION OF RESERVOIR CAPACITY Fig. 3.9 shows the enlarged view of the curve from period 1967 to 1971 during which maximum storage is required. Line AB is drawn parallel to demand curve and tangential to the mass inflow curve at point 4. At point C of the curve, a storage capacity of 1.6 million hectare metres is required. It is essential that the demand line AB should meet the inflow. curve at point B, so that reservoir becomes full at B ; otherwise it will never be full. Similarly, if a line CD is drawn parallel to the demand curve, and tangential to the mass-inflow curve at C, then it should intersect the curve at D so that the reservoir becomes full at the start of the dry period.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.52 WATER SUPPLY ENGINEERING The most common types of non-rigid dams are : (i) earth dam (ii) rockfill dam (ii) combined earth and rockfill dam. 1. GRAVITY DAMS A gravity dam is the one in which the external forces (such as water pressure, wave pressure, silt pressure, uplift pressure etc.) are resisted by the weight of the dam itself. Thus the forces disturbing the stability of the dam are resisted by the gravity forces of the mass of the dam. A gravity dam may be constructed either of masonry or of concrete. Masonry gravity dams are now-a-days constructed of only small heights. All major and important gravity dams are now constructed of concrete only. A gravity dam may be either straight or curved in plan. Fig. 3.11 shows a gravity dam, which may be subjected to the following ‘orces : (i) water pressure P, (ii) weight of the dam, W, (iii) uplift- pressure, U, (iv) pressure due to earth quake, P., (¥) ice pressure, Pi, (vi) wave pressure, P., and (vii) silt pressure P, A moderate size gravity dam may have a drainage/inspection gallery. Most of the gravity dams are solid so that no bending stress is introduced at any point. Gravity dams are particularly suited across gorges with very steep side slopes where earth dams might slip. Where good foundations are available, gravity dams can be built upto any height. The highest dam in the world are of gravity type. FIG. 3.11. GRAVITY DAMSURFACE SOURCES ' 53 2. ARCH DAMS Anarch dam (Fig. 3.12) is adam curved in plan and carries a major part of its water load horizontally to the abutments by arch action. This part of water load depends primarily upon the amount of SECTION AT ¢ FIG. 3.12. ARCH DAM curvature. The balance of the water load is transferred to the foundation by cantilever action. The thrust developed by the water load carried by arch action, essentially requires strong side walls of the canyon to resist the arch forces. The weight of arch dam is not counted on to assist materially in the resistance of external loads. For this reason, uplift on the base is not an important design factor. 3. BUTTRESS DAMS A buttress dam (Fig. 3.13) consists of a number of buttresses or piers, dividing the space to be dammed into a number of spans. To hold up water and retain the water between these buttresses, panels are constructed of horizontal arches or flat slabs. When the panels consist of arches, it is known as muliple arches type buttress dam. If the panels consist of flat slab, it is known as deck type buttress darn. \ 4. STEEL DAMS 1 Steel dams are constructed with a framework of steel with a thin skin plate as deck slab on the upstream side. In India, no such dam has been constructed. However, in United States three such dams have been constructed : Ash Fork Dam in Arizona (1898), Redridge Dam in Michigan (1905) and Hauser Lake Dam in Montana (1901). Out of these, the first two dams gave satisfactory results34 WATER SUPPLY ENGINEERING " SECTION AT AA SECTIONAL ELEVATION — PLAN (a) DECK TYPE (b) MULTIPLE ARCH TYPE FIG. 3.13. BUTTRESS DAMS while the third dam failed only after one year of service. The failure was mainly due to undermining of the foundation by leakage through or under the steel sheet pile. Steel dams (Fig. 314) are generally of two types : (i) direct strutted type and (ii) cantilever type. In the direct strutted type, the load on the deck plate is carried directly to the foundations through ZN AN (a) DIRECT STRUTTED TYPE (b) CANTILEVER TYPE FIG. 3.14. STEEL DAMSSURFACE SOURCES 5S inclined struts. In the cantilever type, the section of the bent supporting the upper part of the deck is formed into a cantilever truss. This arrangement introduces a tensile force in the deck girders which is resisted dither by anchoring the deck girder into the foundation at the upstream toe or by framing the entire bent rigidly together so that the moment of the weight of the water on the lower part of the deck may be utilized to offset the moment of the cantilever. 5. TIMBER DAMS A timber dam is constructed of framework of timber struts and beams, with timber plank facing to resist water pressure. A timber dam is an ideal temporary dam, though a well designed, con- structed and maintained timber dam may last 30-40 years. They are suitable to places where timber can be available in plenty. Timber dams are normally found to be of three types : 1. A-frame type (Fig. 3.15). 2. Rock-filled crib type (Fig. 3.16) 3. Beaver type. 1. A frame type timber dam Fig. 3.15 shows a typical A-frame type timber dam. It consists of five component parts : (a) sills (6) struts (c) wales (d) studs and (e) lagging. The sills should be fastened to the ledge rock by wedge bolts or anchor bolts. The lagging should not be of less than S cm thickness. FIG. 3.15. A-FRAME TYPE TIMBER DAM 2. Rockfilled crib type timber dam Fig. 3.16 shows such a type of dam in which cribs of square or round timber are drift-bolted together. The timbers are spaced about 2-2.5 m centre to centre both ways. The space between them is filled with rock fragments or boulders. In the case of rock foundation, the bottom cribs are pinned to the rock foundation. If, however, the dam is constructed on earth foundation, sheet piling is provided both at the u/s as well as d/s side as shown in Fig. 3.16.56 WATER SUPPLY ENGINEERING D/S CUTOFF FIG, 3.16. ROCKFILLED TIMBER CRIB DAM. 3. Beaver type timber dam Fig. 3.17 shows Beaver type timber dam which is the lowest in cost if plenty of timber is available. This is used only for low height and u/s slope of the dam is not kept steeper than 1 in 2. It consists of a number of timbers the butts of which point downstream, and between the butts are placed spacer logs which are drift-pinned. Fill of earth or sand is placed over the plank deck for its stability. . FIG. 3.17. BEAVER TYPE TIMBER DAM 6. EARTH DAMS AND ROCKFILL DAMS Earth dams are made of locally available soils and gravels, and are therefore most common types of dams used upto moderate heights. Their construction involves utilization of materials in the natural state requiring a minimum of processing. With the advancing knowledge of soil mechanics and with the advent of more sophisticated earth moving equipment, earth dams are now becoming more common, even for higher heights. The foundation requirements of earth dams are less stringent than for other types. Fig. 3.18 (a) shows a typical section of composite earth dam. A rockfill dam is an embankment which uses variable sizes of rock to provide stability and an impervious membrane to provide water tightness. In modern practice, the rockfill dam has four fun-aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.60 WATER SUPPLY ENGINEERING The lowest entry is placed below the low water level of the river so that water is available in the jack well during summer season also when river carries minimum discharge. The intake well should be founded on sound footing, to a depth deeper than the scour depth. The upper part of the well serves as the pump house. The suction pipe admits water through a screen. Where river bed is soft or unstable, the intake tower may be founded slightly away from the river bed, as shown in Fig. 3.20. The intake is kept submerged under the low water level of the river. It essentially consists of a rectangular or circular entry chamber with a Strong grill at its top. The pipe conveying water from the intake to the jack well has a bell-mouth entry with a screen, and is supported on a concrete support. While the entry of debris and floating material is checked by the top grill, the entry of mud or coarse sand etc. is checked by the screen provided at the bell-mouth entry. Water enters to the jack well through a valve which can be controlled from the pump house. Reservoir Intake When the flow in the river is not guaranteed throughout the year, a dam is constructed across it to store water in the reservoir so formed. The reservoir intakes are practically similar to the river intake, except that these are located near the upstream face of the dam where maximum depth of water is available. Their design depends upon the type of dam. Fig. 3.21 (a) shows a typical intake for an earth dam with several entry ports. The intake is constructed near the toe of the dam. The access to the intake tower is provided through a foot bridge. Water may enter the well through a number of entry ports located at various elevations so that relatively clear top water is admitted at all seasons. The water level in the well is practically the same as the reservoir level. The valves of the entry ports are operated from the gate house located at the top of the well. From the well, water is led to the down-stream through a suitably designed conduit which passes through the body of the earth dam. Fig. 3.21 (6) shows the dry type intake well with a trash-rack structure which is located below the minimum reservoir level. The entry of water is controlled through a valve operated from the upper portion of the well. Fig, 3.21 (c) shows an alternative form of the dry well in which water from different entry ports is led directly to the outlet pipe. The well remains dry. In each case, however, the outlet pipe or conduits passes through the main body of the earth dam. This pipe, commonly known as the sluice way, should have projecting collars at regular intervals. These collars increase the path of water seeping along the boundary of the sluice way. The length of the seepage path should be more so that no damageaa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.water canal WATER SUPPLY ENGINEERING: Solution 1. Discharge through intake Daily discharge= 150 x 80000 = 12000000 1/ day. Since the canal runs only for 10 hours per day, Intake loadfhour = 1220009 — 1209000 1, hr = 1200 m'/hr _ 1200 | 3 Q =x = 0.3333 m’/sec. 2. Area of coarse screen in front of intake Area of screen, As = @ _ 0.3333 « 9.083 m? v 0.16 Let the area occupied by solid bars be 30% of the total area. ~. Actual area of screens = 2.083/0.7 = 2.98 m? Let as assume minimum water level at 0.3 m below normal level. Also, let us keep bottom of screen at 0.2 m above bed and top of screen at the minimum water level. ~. Available height of screen= 1.8 — 0.3 -0.2=13 m . Required length of sereen= 238 = 2.29 m Hence provide length= 2.3 m Hence provide screen of size=13mx23 m 3. Design of bell mouth entry Area of bell mouth, y= 99333 = 1.042 m* Dia. do = V ion x4 =115 m. Hence provide bell mouth of 1.2 m diameter. 4, Design of intake conduit Let us assume a velocity of 15 m/sec in the conduit. -. Dia. of intake conduit, D = J ee 333) xf = 0.532 m However, provide 0.5 m dia. conduit, so that actual velocity of flow isSURFACE SOURCES 65 _ 0.3333 x 4 (0.5)? For head loss through the conduit, consider Eq. 16.10 : V =0849CR° 9, Take C = 130 for cast iron pipes Also, R=D/4=05/4 =0125 m. Hence slope S of the energy line is given by 1.7 = 0.849 (130) (0.125)"". s*™ = 1.7 m/sec. or 1.7 = 29.779 . 17 0st ay From which S= (soqa5 = 4.98 x 10 But S=H/L ©. Hence loss Hy =S.L = 498 x 107*(3 x 1000] = 249m For the arrangement of various components of the canal intake, refer Fig. 3.24. PROBLEMS 1. Describe in brief various investigations required for reservoir planning. 2. What are the factors on which the selection of the site of a reservoir depend ? 3. What do you understand by mass inflow curve and how it is prepared? 4. What do you understand by demand curve ? Explain the method of calculating reservoir capacity for a specified yield, from the mass inflow curve. 5. Explain how do you determine the safe yield from a reservoir of a given capacity. 6. Classify various types of dams. Discuss in brief merits and demerits of various types of dams. 7. Discuss the physical factors that govern the selection of. type of dam. 8. What are intakes ? What are the important considerations which govern the selection of site of an intake. 9. Describe the river intake and reservoir intake. 10. Describe the working of a canal intake. 11. Describe, with the help of sketches, a reservoir intake for an earth dam.Ground Water : Wells 4.1L. INTRODUCTION Ground water hydrology is the science of the occurrence, dis- tribution and movement of water below the surface of carth. The largest available source of the fresh water lies underground. The total ground water potential is estimated to be one-third the capacity of oceans. The main source of ground water is precipitation. A portion of rain falling on the earth’s surface infiltrates into ground, travels down and when checked by impervious layer to travel further down, forms ground water. The ground water reservoir consists of water held in voids within a geologic stzatum. Other sources of ground water include water from deep in the earth which is carried upward in intrusive rocks and water which’ is trapped in sedimentary rocks during their formation. The quantities of such waters aré small and they are often so highly mineraliséd-as to be unsuited for use. Water bearing formations of the earth’s crust act as conduits for transmission and as revervoirs for storage of ground water. The discharge from ground water occurs in two ways : (1) natural way (2) artificial way. The natural discharge occurs as flow in lakes, reservoirs, rivers oceans and springs. Pumpage from wells constitutes the major artificial discharge of ground water. 4.2, TYPES OF AQUIFERS Aquifers are mainly of two types : 1. Unconfined aquifer. 2. Confined aquifer (artesian aquifer). (66)GROUND WATER : WELLS 67 Unconfined Aquifer Unconfined aquifer, or water-table aquifer is the one in which a water table serves as the upper surface of the zone of saturation. It is also sometimes known as the free, phreatic or non-artesian aquifer. In such an aquifer, the water table varies in undulating torm and in slope. Rises and falls in the water table correspond to changes in the volume of water in storage within the unconfined aquifer. ARE, Au rplehen tase wens ARTESIAN WELL FIG. 41. CONFINED AND UNCONFINED AQUIFERS. Confined aquifer or artesian aquifer Confined aquifer or artesian aquifer is the one in which ground water is confined under pressure greater than atmospheric by overlying, relatively impermeable strata. Artesian aquifers are analogous to pipelines. The static pressure at a point within the artesian aquifer is equivalent to the elevation of the water table in the recharge area less the loss in head through the aquifer to the point under consideration. In a well penetrating such an aquifer, the water level will rise to the level of the local static pressure or artesian head. Water enters a confined aquifer in an area where the confining bed rises to the surface or ends underground and the aquifer becomes unconfined. Artesian aquifers usually have relatively small recharge areas as compared with unconfined aquifers. When water is withdrawn from an artesian well, a local depression of the piezometric surface results. This decrease in pressure permits a slight expansion of the water and in some cases a compaction of the aquifer.6 WATER SUPPLY ENGINEERING Flowing well and Artesian well When a well penetrates a confined aquifer, water rises in the well to the level of local static pressure or artesian head. If this artesian pressure is sufficient to raise the water above the ground level, a flowing well occurs, such as well A in Fig. 4.1. If however, the water level in such a well is below the ground level, but is above the local water table, it is known as the artesian well, such as well B in Fig. 4.1. Perched Aquifer Perched aquifer (Fig. 4.2) is a special type of unconfined aquifer, and occurs where a ground water body is separated from the main ground water by a relatively impermeable stratum of small aerial extent and by the zone of aeration above the main body of ground water. TORI TRIER TNT INE YF EVIRG IT RI IITA, {PERCHED WATER TABLE IMPERME, — DETERTABLE__ AQUIFER IVTITTITTITT TTI I TIT IT ITI ROCK FIG. 4.2. PERCHED AQUIFER 4.3, STORAGE COEFFICIENT ‘The water yielding capacity of a confined aquifer can be expressed in terms of its storage coefficient. Storage coefficient is defined as the volume of water that an aquifer releases from or takes into storage per unit surface area of aquifer per unit change in the compo- nent of head normal to that surface. Let us consider a vertical column of unit area (one metre X one metre ) extending through a confined aquifer (Fig. 4.3). Then the storage coefficient, S, is the volume of water, in cubic metres, teleased from the equifer when the piezometric surface declines by one metre. In most of the confined aquifers, the value of storage coefficient ranges between 0.00005 to 0.005. Its value can be determined from pumping tests of wells penetrating fully into confined aquifer. In an unconfined aquifer, when the water table is lowered ‘by one metre, the water from 1 metre height of the vertical columnGROUND WATER : WELLS oo PIEZOMETRIC “SURFAC CONFINED AQUIFER FIG. 4.3. STORAGE COEFFICIENT of unit area drains freely under gravity. Thus, storage coefficient for an unconfined aquifer corresponds to its specific yield. Coefficient of permeability (k) The coefficient of permeability is defined as the velocity of flow which will occur through the total cross-sectional area of the soil (or aquifer) under a unit hydraulic gradient. Some typical values of the coefficient of permeability are given in the table below : TABLE 4.1 Soil type Coefficient of permeability emlsee Clean gravel 1.0 and greater Clean sand (coarse) 1.0-0.01 Sand (mixture) 0.01-0.005 Fine sand 0.05-0.001 Silty sand 0.002-0,0001 Silt 0.0005—0.00001 0.000001_and_smailer Coefficient of Transmissibility (7) Coefficient of transmissibility is defined as the rate of flow of water (in m’/ day or gallons/day) through a vertical strip of aquifer of unit width (1 m or 1 ft) and extending thé full saturation height under unit hydraulic gradient, at a temperature of 60° F.7m WATER SUPPLY ENGINEERING Thus, the coefficient of transmissibility T equals to the field coefficient of permeability multiplied by the aquifer thickness (B): T = Bk. 44, WELL HYDRAULICS Darcy's Law. The percolation of water through soil was first studied by Darcy (1856) who demonstrated experimentally that for laminar flow conditions in saturated soil, the rate of flow or the discharge per unit time is proportional to the hydraulic gradient, and it could be expressed as follows : Q=kiA +-(4.1) =Qaki or ve ki (4.2) where Q=rate of flow i= hydraulic gradient k = Darcy's coefficient of permeability A = total cross-sectional area of soil mass perpen- dicular to the direction of flow v = flow velocity. Eq. 4.2 demonstrates the linear dependency between the hydr- aulic gradient and the discharge velocity. However, it in no way describes the state of affairs within an individual pore. Strictly speaking, Darcy’s law represents the statistical macroscopic equivalent of the Navier-Stokes equation of motion for the viscous flow of ground water. Darcy's law is valid only for laminar flow. Because of very small pore dimensions in fine grained soils, a laminar flow should exist, but in coarse grained soils, turbulent flow may be expected under certain conditions. It has been borne out by experiments that the limits of validity of Darcy’s law may be fixed with respect to particle size, velocity of flow and hydraulic gradient. Fancher, Lewis and Barnes demonstrated that flow through sands remains laminar and the Darcy’s law valid so long as the Reynold’s number, expressed in the form below is equal to or less than unity : eee <1 (43) where p = mass density # = dynamic viscosity d =diameter or particle size v =velocity of flow.GROUND WATER : WELLS a For the ground water flow occurring in nature, the law is generally within its validity limits. But in rock aquifers, in un- consolidated aquifers with the steep hydraulic gradients, or in those containing large diameter solution openings, Darcy’s law may not be applicable. Also, the flow in the immediate vicinity of wells have steep hydraulic gradient and the Darcy’s law is not applicable in the immediate vicinity of the well. STEADY RADIAL FLOW TO A WELL : DUPUIT’S THEORY When a well is penetrated into an extensive homogeneous aquifer, the water table initially remains horizontal in the well. When the well is pumped, water is removed from the aquifer and the water table or piezometric surface, depending upon the type of the acquifer, is lowered resulting in a circular depression in the water table or the piezometric surface. This depression is called the cone of depression or the drawdown curve. At,any point, away from the well, the drawdown is the vertical distance by which the water table or the piezometric surface is lowered. The analysis of such radial flow towards a well was originally proposed by Dupuit in 1863 and later modified by Thiem (1906). For the sake of analysis, we shall take two cases : (1) well in unconfined aquifer, and (2) well fully penetrating a confined aquifer. (1) Unconfined Aquifer OBSERVATION WELLS IMPERVIOUS LAYER FIG. 4.4. UNCONFINED AQUIFER72 WATER SUPPLY ENGINEERING Fig. 4.4 shows a well penetrating an unconfined or free aquifer to its full depth. Let r=radius of the well H =thickness of the aquifer, measured from the impermeable layer to the initial level of water table s = drawdown at the well A =depth of water in the well, measured above the impermeable layer. Considering the origin of co-ordinates at point O at the centre of the well at its bottom, let the co-ordinates of any point P on the drawdown curve be (4%, y). Then, from Darcy's law OH=kAi, where Az = area of cross-section of the saturated part of the aquifer at P = (2x2) x () =2ary is = hydraulic gradient at P = 2 = dy Hence Q=k(2xxy) x Q a =2aky.dy. Integrating between the limits (R, 7) for x and (H, h) for y, we get of Sr f" yw r = h R= a Q (logex)F ane [¥ lk From which ak (H® — h®) _ 136k (H? — h*) Qu TEA) _ 136k K) wl4.4) loge x logio x If k (coefficient of permeability) is expressed in cubic metres per day per square metre (m’/day/m’) of the area of sub-soil, the above expression for discharge will directly be in cubic metres per day (m’/day) units. If, however, x is in gallons per day per sq. foot of area of sub soil, the discharge will be in gallons per day.GROUND WATER: WELLS 3 In the above expression, R, commonly known as radius of zero drawdown, is the radius, measured from the centre of the well to a point where the drawdown curve meets the original water table tangentially. In practice, the selection of the radius of influence R is approximate and arbitrary, but the variation in Q is small for a wide range of R. Suggested values of R fall in the range of 100 to 300 metres. Alternatively, R may be computed from the following approx- imate expression given by Sichardt : R = 3000sVk where R and s are in metres, and & is in m/sec. If there are two observation wells at radial distance r,; and 1, (% > 1) , and if the depths of water in them are A, and fh; respectively, Eq. 4.4 can also be expressed in the form : Q- 25-8) (44 a) loge ai or Q = 136k (Hi hi) (44 b) logios= If the drawdown (s) is measured at the well, we have s=H-h and H=st+h, or H+h=(s + 2h) Then, from Eq. 4.4, g= ZAM +h) aks (s+ 2h R R loge i loge or Q= aks (5 1) = aks (L +) loge = loge > where h =L = Length of the strainer or o= 272ks (L + s/2) wn(4.5) togw® Assumptions and Limitations of Dupuit’s Theory Dupuit’s theory of flow for unconfined aquifer is based on the following assumptions : 1, The velocity of flow is proportional to the tangent of the hydraulic gradient instead of sine. 2. The flow is horizontal and uniform everywhere in the vertical section.74 WATER SUPPLY ENGINEERING 3. Aquifer is homogeneous, isotropic and of infinite aerial extent. 4. The well penetrates and receives water from the entire thickness of the aquifer. 5. The co-efficient of transmissibility is constant at all places and at all times. 6. Natural ground water regime affecting an aquifer remains constant with time. 7. Flow is laminar and Darcy’s law is applicable. Out of these, assumptions (1), (2) and (7) are of particular importance. The flow is not horizontal, especially near the well. Also, the piezometric surface attains greater slope as it approaches the well boundary, with the result that assumption 1 is an approximation. Due to these reasons, the parabolic form of piczometric surface computed from the Dupuit’s theory deviates from the observed surface. This deviation is large at the well face, resulting in the formation of seepage face. In addition to these, the velocity near the well increases and the flow no longer remains laminar. Thus, Darcy’s law equation is not valid near the well face. 2. Confined Aquifer Fig. 4.5 shows a well fully penetrating a confined or artesian aquifer. Let (, y) be the coordinates of any point P on the drawdown curve, measured with respect to the origin O. Then, from Darcy’s law, flow crossing a vertical plane through P is given by Q=kirAr where Ax = cross-sectional area of flow, measured at P = 2a0xb 6 = thickness of confined aquifer i, = hydraulic gradient at p=% =k(% Q=k ( a) (2"xb) Q% =22kb.dy. Integrating between the limits (R,r) for x and (H, h) for y, we get Q f &-rsk0f 4 x . ‘ i Lh O[logex]® =22kb[y|aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.16 WATER SUPPLY ENGINEERING If A, and 2 are the measured depths of water in two obser- vation wells situated radially at distances r; and r; respectively, the above equations can also be expressed as = 272d k (ta - hi) _ 272 Te -m) (46 e) loge log? If Ay is the depth at any radial distance x, the discharge can be written as = 2akb (hy = h) loge Equating this to Eg. 4.6 (a), we get loge = hy —h =(H—A) 2 (4.7) loge This shows that head varies linearly with the logarithm of distance regardless of rate of discharge. 4.5. DETERMINATION OF AQUIFER CONSTANT T (a) Confined Aquifer The aquifer constant T (cofficient of transmissibility) can be determined by a pumping out test, and by observing drawdowns at various observation wells. Pumping must continue at a uniform rate for a sufficient time to approach a steady-state condition for which equilibrium equation 4.6 is applicable. Steady-state condition is the one in which the drawdown changes negligibly with time. Refer Fig. 4.5. Let $1 = drawdown in well 1 = (H — fh) $2 = drawdown in well 2 = (H — hz). _ of inh = (A -&) - (H- 51) = 51-5 Then from equation 4.6 (d), o- 2.72T (ha — hi) _ 2.72T (51 — 52) tn nn logu= loge 7 T (48) a Q n TG aay OF, Choosing rm, = 107r;, we find logw =i.GROUND WATER : WELLS 1 DRAWDOWN S ae ne OD . Hence T= 573, >m) LAS (4.9) where As =difference in drawdowns at the two wells so selected that r:= 107, The method, therefore, consists in observing drawdowns 5), 52, Sy at certain observation wells distant 71, r2, ....rx, etc., and plotting a graph between s, as ordinate and logwr, as abscissa, thus getting a straight line as shown in Fig. 4.6. From the graph, As can be obtained for one log cycle of distance and can be substituted in equation 4.9 to get T. (6) Unconfined Aquifer The above method of determination of T can also be extended to an unconfined aquifer. Refer Fig. 4.7. h=H-sy hy =H-52 Whi = (H- 9) -(H-51)" vot 3 =o = 2H (s;' — 52’) where s;' and s;' are modified drawdowns given by 2 sf =s- 3b 2H and oo! = oHB WATER SUPPLY ENGINEERING Now from equation 4.4 (a), _ tk (Ai —hi) _ 136k (hi hi) n fn loge mn logo A 2 Substituting the value of (h}— hj) from above, we get o- 1.36 [2H (s1' — 92')] log? _ 2.72kH(s;' ~s') th logis Since H = aquifer thickness, we have KH = T o 222. bre S2') logw 52 From which = Q n T= Say et (4.10) a S MODIFIED ORAWDOWN Ss’ On 2 o o ' 10 100 1000 FIG. 47. It should be noted that equations 4.8 and 4.10 are identical. Choosing r2= 107 as before, we get enn. Te (411) Thus, the observed drawdowns are corrected or modified, and a graph is plotted between the modified drawdown (s") and logarithm of distance of observation wells from the discharge well. Measuring As’ for one log cycle of distance, we get T from equation 4.11.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.80 WATER SUPPLY ENGINEERING For a screen which is not clogged or encrusted and whose size is compatible to the surrounding porous media, the portion of the well loss caused by water entering the well is small in comparison with the portion resulting from axial movement inside the well to the pump intake. Specific Capacity The specific capacity of a well is the measure of the effectiveness of the well, and is defined as the yield of the well per unit drawdown. Thus, if s = drawdown Q=well discharge or the yield. Then, specific capacity =2 For a confined aquifer, from equation 4.12, we have 5 =BQ+CQ”" Hence, Specific Capacity is = =—1 4.3 BQ+CQ" B+cQ" This shows that the specific capacity of a well is not constant, but decreases as discharge increases. 4.7. INTERFERENCE AMONG WELLS When two wells, situated near to each other, are discharging, their drawdown curves intersect within their radius of zero drawdown. Thus, though the total discharge is increased, the discharge in individual well is decreased due to interference. Fig. 4.9 shows interference between two wells. If the two wells are a distance B apart, and have the same diameter and drawdown and discharge over the same period of time, it can be shown with the help of method of complex variables, that the discharge through each well is given by FIG. 4.9. INTERFERENCE BETWEEN TWO WELLSGROUND WATER : WELLS 81 Qa= ee) wu(4.14) loge &, 7B ’ where R is the radius of area of influence (R >> B). If there were only one well, then the discharge, under the same drawdown, would have been, from equation 4.6 (a), — 2akb ue h (4.6 @) loge ® Since R> B, HR Hence Q>Q. Thus, discharge in each well decreases due to the interference. Similarly, if there are three wells forming an equilateral triangle a distance B on a side, and if all the three wells have the same characteristics, Q: = Q, = Q, = SRO Hh) w(4.15) loge OB rB? 4.8. FULLY PENETRATING ARTESIAN-GRAVITY WELL Sometimes, in an artesian well (ie., a well in a confined aquifer) high pumping rates may lower the water at the well face to a level below the top of the confined aquifer, as shown in Fig. 4.10. In such a case, the flow pattern close to the weil is similar to that GROUND SUREOS £ INITIAL, PIEZOMETRIC SURFACE IMPERVIOUS LAYER FIG, 4.10. ARTESIAN-GRAVITY WELL82 WATER SUPPLY ENGINEERING: for a gravity well (Le. a well in unconfined‘aquifer) whereas at distances farther from the well, the flow is artesian. This type of well is known as a combined artesian-gravity well. Fig. 4.10 shows an artesian gravity well. The flow from such a well-can be computed from the following expression developed by Muskat : 2 2, o=atGw-# =" ibe) loge 4.9. PARTIALLY PENETRATING ARTESIAN WELL A partially penetrating artesian well is the one in which the well screen does not penetrate to the full depth of the confined aquifer. The pattern of flow in the aquifer in the vicinity of such a well deviates from that for a fully penetrating well. In practice, we often encounter such wells that extend only part way through the water bearing strata. Fig. 4.11 shows a partially penetrating artesian well in which the strainer length b, is less than the aquifer thickness 6. The discharge Qp from such a well can be computed from the following equation: OQ, = MHD G=0.6 (4.16 b) loge where Q, = discharge for the partially penetrating well. ‘CONE OF DEPRESSION It coneinco AQUIFER ©. - IMPERVIOUS LAYER FIG. 411. PARTIALLY PENETRATING ARTESIAN WELLGROUND WATER : WELLS 83 Q=discharge for a fully penetrating well for the same drawdown (H ~ h). G =correction factor for partial penetration =2 Q A reasonable estimation of the correction factor G can be obtained from the following expression developed by Kozeny : = (4m cos™ G=s 1+7 a, 8 35 4.10. SPHERICAL FLOW IN A WELL Fig. 4.12 shows a special case of partially penetrating well, where the well just penetrates the top surface of a semi-infinite porous medium. Here 5; =0, and equation 4.16 does not apply because the flow towards the well is purely spherical. The discharge Q; from such a well can be computed from the expression Q, =2akr(H —h) (4.18) For the case of simple radial flow in a fully penetrating well, the discharge Q is given by equation 4.6 (a) : oO = Hh) (4.6 a) loge R (4.17) v INFLUENCE: - . ” IMPERVIOUS STRATUM FIG. 4.12. SPHERICAL FLOW IN A WELL84 WATER SUPPLY ENGINEERING g = Log. © = 2.303 F tog (4.19) As a numerical example, Let r=8cem = 008m ~ 1000 b = thickness of aquifer = 16 m. Qs 7.303 x 2:08 eek o = 2.303 x 16 Logie 1000 = 57. This shows that the spherical flow is very much less efficient than the radial flow. 4.1L. TUBE WELLS A water well is a hole or shaft, usually vertical, excavated in the earth for bringing ground water to the surface. Wells can be mainly divided into two classes. 1. Dug wells or open wells. 2. Bored or drilled wells or tube wells. An open weil is comparatively of bigger diameter and is suitable for discharges upto 0.005 cumec. This is because the cross-sectional area of flow is less in the open well, and the water can be withdrawn safely only at the critical velocity for the soil. A tube weil is a long pipe sunk into the ground with a strainer which allows water to pass through but prevents sand from coming in. Because of the strainer, high velocity of flow can be permitted without danger of soil particles being carried away with water. Also because of the radial flow towards the well, the cross-sectional area of flow is more. Due to the increased velocity and more cross-sectional area of flow, a.tube well, though much less in diameter than an open well, gives discharge many times more than the open well. Types of Tube wells Tube wells may be of three types : 1, Strainer well. 2. Cavity well. 3. Slotted well. 1, STRAINER TYPE TUBE WELL The strainer well is the most common and.widely used tube well. In common term, the word "tube well” refers to the strainer type of tube well. In this type of well, a strainer, which is a specialGROUND WATER: WELLS 85 type of wire mesh, is wrapped round the main tube of the well. The main pipe contains bigger holes or slots than the openings of the strainer. The total area of the opening of the tube is képt equal to the openings of the strainer so that the velocity of flow does not change. Due to fineness of the openings of the strainer, a higher operational velocity of water can be permitted. Little annular space is left between the strainer and the pipe so that the open area of pipe perforations is not reduced. The mesh size of the strainer is generally kept equal to Dw to Dy» of the surrounding soil. GROUND SURFACE aon TEE TOBLE Z.. CONFINED AQUIFER- , STRAINER © > IMPERVIOUS LAYER FIG. 4.13. STRAINER TYPE TUBE WELL. A strainer well may draw water either from an unconfined aquifer of unlimited extent, or from one or more confined aquifer layers. The strainers are provided only in that length of the pipe where it crosses the aquifer. The pipe in the aquifer portion is kept perforated. In the rest of the portion, plain or blind pipe is provided. At the bottom, a short blind pipe is provided to permit settlement of any sand if passed through the strainer. The well is generally plugged at the bottom. Abyssinian tube well is a special type of strainer tube well, in which the diameter of pipe is kept ly and the strainer is provided only for a length of about 4 to 5 feet. Design criteria for strainer type tube well The following points should be noted for the design of a Strainer type of tube well : (1) The wire screen should not be in contact with the slotted tubes otherwise a large part of the opening will be covered by the wire screen.86 WATER SUPPLY ENGINEERING (2) The area - of the opening in the wire screen should be equal to the area of waterway in the perforated or slotted tube to permit no change in the velocity of incoming water particles. If there is any change, sand will be deposited in the annular space. (3) The design should permit less velocity through soil than the exit critical velocity which is 1.25 cm/sec. (4) The discharging velocity should vary from 1 mjsec to 2 misec. (5) The total surface area of tube well should be more than three times the area of perforations. (6) The material of the strainer (wire screen) should be such that it can withstand the strain of sinking and at the same time can give maximum amount of waterway consistent with fineness of opening necessary to prevent entry of sand. (7) The material should preferably be of one metal. A bimetal construction pose a danger of electrolytic action in water, which may ultimately lead to deposition of salt and chocking of openings. (8) The material should be sturdy and withstand rough handling. Following metals and alloys have been found useful for strainers. They are corrosion-resistive : @ Zinc-free-brass or cupro-nickel alloy. (ii) Stainless steel. (iii) Low carbon steel. (iv) High copper-alloy. Types of Stainers Following are some of the common types of strainers used in tube wells : ( Cook strainer. (i) Tej strainer. (ai) Brownlie strainer. (iv) Ashford strainer. (v) Leggett strainer (vi) Phoenix strainer. (vii) Layne and Bowler strainer (1) Cook strainer : This is a very costly strainer of American patent. It is made up of solid drawn brass tube slotted with wedge-shaped horizontal slots. The slots are made with a slot cutting machine from insideGROUND WATER: WELLS the tube. The slots are wide inside and narrower outside, as shown in Fig. 4.14. The gauge of slots depends on the coarseness of sand, and varies from 0.15 to 0.4 mm. (ii) Tej strainer It is similar to cook strainer, but is manufactured in India. It con- sists of a brass tube constructed of a brass sheet bent round to form the tube, the vertical joint being brazed. The slots are cut in the sheet before it is bent. The strainer is generally manufactured from 7.5 cm diameter FIG. 4.14. COOK STRAINER upwards, and is made in 25 metre lengths. The individual lengths of the strainer are then joined together by means of screwed collars of brass. (iii) Brownlie strainer The Brownlie strainer is made of plate having perforations. A wire mes! as shown in Fig. 4.15. The mesh consis a polygonal convoluted steel h surrounds the steel tube, ists Of heavy parallel copper wires woven with copper ribbons. Since the wire mesh is slightly away from the perforated tube, it is known as the best type of strainer. FIG. 4.15. BROWNLIE STRAINER (i) Ashford strainer This is very delicate strainer and consists of perforated tube with a wire round it over which a wire mesh is soldered. The wire88 WATER SUPPLY ENGINEERING keeps the mesh away from the tube. The wire mesh is protected and strengthened by a wire net around it, as shown in Fig. 4.16. (v) Leggett strainer It is expensive type of strainer in which a cleaning device is provided. The cleaning device cae THE TUBE is in the shape of cutters which « {ide PERFORATED can be turned in the slits. The cH TUBE cutters are operated from the top (ground surface), These cutters clean the strainer clogged by the solid matter. (vi) Phoenix strainer It is a mild steel tube in which the openings are made by cutting slits from inside. The tube is cadmium plated to keep it free from danger of chocking and corrosion caused by chemical action. (vii) Layne and Bowler strainer It is a robust type strainer manufactured in America. It consists of wedge-shape steel wire wound to suitable pitch round a slotted or perforated steel or wrought iron pipe. The joint of the straincr pipes are made by screwed collars. Chocking of Strainers The strainer of a tube well may get chocked due to two actions: (1) Mechanical action, (2) Chemical action. (1) Mechanical chocking. Mechanical chocking may result from the chocking of slits with sand and other particles. This may however, be prevented by providing such slits which expand inwards. The pulsating action of the centrifugal pump may also remove the chocking. To safeguard against chocking, proper screening or shrouding should be provided. Another method of eliminating chocking is to permit inflow velocity lesser than the critical. ’ (2) Chemical chocking. The strainer may be chocked due to chemical action of salts present in water. The chemical action may also deteriorate a strainer by corrosion. If calcium bicarbonate present in water exceed by an amount of 15 parts per million parts of water, carbon dioxide is released when pressure is reduced due to pumping and calcium carbonate is precipitated on the strainer. The cumulative action of such precipitation reduces the yield. The chemical chocking FIG. 4.16. ASHFORD STRAINERaa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.GROUND WATER: WELLS 1 by a depth of about 5 m length. The perforated pipe, sometimes known as the education pipe, of 15 cm diameter is then lowered, the slotted portion being only 5 m long and the rest of the length being of plain pipe. Gravel is then poured from the top, upto about 3 to 4 m higher than the top level of perforated portion of the pipe. The casing pipe is then withdrawn 5 cm at a time and the well is developed with the help of compressed air pumped into the education pipe. Finally, when the casing pipe is fully withdrawn, the annular space between the casing pipe and the education pipe is suitably plugged. By developing the well with the help of compressed air, the sand surrounding the gravel filter is freed of finer particles and the chances of getting the filter chocked are reduced. Due to the provision of gravel shrouding, a larger area of radial flow is obtained. There are two essential differences between a strainer tube well and a slotted tube well : (1) in the strainer tube well, the strainer pipes are surrounded by wirc mesh to prevent the fine particles from entering the well, while in the slotted tube well the gravel shrouding serves this purpose, (2) a strainer tube well may have several alternative lengths of strainer pipes and plain pipes, while a slotted tube well has the slotted pipe length only at its bottom. Thus, a strainer tube well draws water from several aquifers sandwiched between impervious layers, while a slotted tube well draws water only from one pervious stratum which has sufficient water bearing capacity. 4.12. METHODS FOR DRILLING TUBE WELLS For installing a tube well in the ground, so as to penetrate the required stratum, a hole, slightly of larger diameter than the diameter of the strainer pipe, is bored. The most common methods for boring a well are : 1. Wash boring or water-jet boring method. 2. Cable tool method (also known as percussion or standard method) 3. Hydraulic rotary method. 4. Reverse rotary method. 1, WASH BORING OR WATER JET BORING METHOD This method is suitable at places where the well is to be sunk into formation consisting of gravel, sand, clay or other soft deposits. The boring is done by cutting action of a downward-directed Stream of water. The outer casing is first erected, in position in a suitable pit dug at the surface. A jet pipe with a nozzle is then lowered in the casing tube, and water under pressure is forced through it. The dislodged soil particles and broken rock pieces form slurry with water and are lifted up through the annular space between92 WATER SUPPLY ENGINEERING SELF JETTING WELL POINT FIG. 4.19. SELF-JETTING WELL POINT the casing and jet pipe by the returning water in the upward direction. The casing pipe having shoes at the bottom is kept rotated slowly, and is thus lowered. In penetrating clays and hard pans, various types of jetting drill bits are fitted to the drill pipe which is raised and lowered sharply, causing the bit to shatter the formation. When the casing pipe has penetrated to a sufficient depth into the aquifer, the well pipe attached with screen ctc. is lowered in the casing pipe. The outer casing is then pulled. Sometimes, a self-jetting well point is uscd. In this, the casing pipe is not used, but instcad, a tube of brass screen ending into a jetting nozzle is screwed to the main well pipe (Fig. 4.19). As the jetting action progresses, the well pipe goes on sinking. An annular space round the well pipe is automatically created due to the upward motion of water carrying the dislodged particles. When the well pipe has been sunk to the desired depth, jetting is stopped and the annular space is packed with gravel. 2. CABLE TOOL METHOD (PERCUSSION METHOD) Cable tool method, alsu sometimes known as the Percussion method or Standard method, is used for drilling deep wells through consolidated rock materials. In this method, a standard well drilling rig consists of a mast, a multiline hoist, a walking beam and an engine—all assembled and mounted on a truck for easy portability. A string of percussion tools consists of (Fig. 4.20) : a rope socket, a set of jars, a drill stem and a drilling bit—the total weight of these amounting to several thousand kilograms. The drilling bits are manufactured in 1 to 3 metre lengths, and may weigh upto 1500 kg. A pit is dug at the site where the well is to be drilled. A casing pipe, with a drive shoe is inserted in the pit. The stringGROUND WATER : WELLS 93 ROPE JARS. ORILL DRILLING BAILER SOCKET STEM BIT FIG. 420. PERCUSSION DRILLING TOOLS of drilling tools is inserted in the first length of the casing pipe. Drilling is then accomplished by regular lifting and dropping of the string of tools mechanically. During drilling, the tools make 40 to 60 strokes per minute ranging from 40 cm to 1m in length. The drilling line is kept continuously rotated so that the drilling bit will form a round hole. After the bit has cut 1 to 1; metre through the formation, the string of tools are taken out and a bailer (Fig. 4.20) is inserted in the hole to remove the drill cuttings. The bailer essentially consists of a pipe like section with a valve at the bottom. When the bailer is inserted in the hole, the valve is automatically opened by the upward movement of the cuttings. The valve, however, prevents the cutting from moving in the downward direction and thus escaping during lifting. When the bailer is full, it is lifted up to the surface and emptied. The length of the bailer varies with its diameter, and may range from 3 to 12 metres. When the cuttings have been taken out, the string of tools are again inserted and blow given to break the formation by impact. If no water is encountered in hole, water is added from the surface to form a paste with the cuttings. The casing is driven down by means of drive clamps fastened to the drill stem. The up and down motion of the tools striking the top of the casing, protected by a drive head, sinks the casing. The individual subsequent lengths of casing are joined by threaded or welded joints. In soft and fissured rock formations, manual labour may be used (Fig. 4.21). In this case, the boring is done with the helpaa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.96 WATER SUPPLY ENGINEERING tency, clay and water is added to the circulating mud from time to time. A complete boring record is maintained to know the type of formations at various depths. When desired level is reached, the drill rod etc. are taken out and the well pipe containing strainer pipes at appropriate locations (opposite aquifers) is lowered. Since the well walls are coated with clay, it should be washed to get more discharge. Back washing is done by lowering the drill pipe and bit in the well pipe, and forcing water containing calgon (sodium-hexa-meta phosphate). Calgon has the property of dispersing clay colloids. A collar, of the size of well-pipe is attached to the drill rod just above the bit. This forces the water through the strainer causing washing action on the clay wall. At the same time, the drill rod is plunged up and down causing surging action. When washing in the bottom is done, the bit is raised through some distance and the operation is repeated. 4. REVERSE ROTARY METHOD Reverse rotary method, similar to the hydraulic rotary method, is very much used in Europe. In this method, the cuttings are used for this purpose. A mixture of water and fine grained material is circulated in the hole. The procedure is essentially a suction dredging method. The walls of the hole during drilling are supported by hydrostatic pressure acting against the film of fine-grained material deposited on the walls by the drilling water. The method of recir- culation of drilling water containing fine-grained particles and cleaning the well after inserting the well-pipe is similar to that of hydraulic rotary methods. 4.13, WELL SHROUDING AND WELL DEVELOPMENT (a) Well Shrouding Well shrouding is a process of interposing coarse material such as gravel and coarse sand between the well-pipe (strainer pipe) and the aquifer soil to prevent finer particles of soil coming in contact with the strainer and chocking it. This is essential in sandy and unconsolidated formations of aquifer. This is also essential in slotted type tube well where a strainer is not used. Such tube well is also sometimes known as a gravel-packed well. The shrouding increases the effective well diameter, acts as a strainer to keep fine material out of the well, and protects the well-pipe from caving of surrounding formations. A gravel packed well has a greater specific capacity than one of the same diameter not surrounded by a gravel. A minimum thickness of 40 cm gravel pack is necessary to make it effective. The proper gain size distribution of the shrouding material depends upon the mechanical analysis of the aquifer and upon the perforations or screen slot size.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.98 WATER SUPPLY ENGINEERING sucks water in. When it is moved down, it‘forces water-calgon solution back in the formation. Further upward motion bring with it fine material. The surge block is connected to a string of hollow pipe from which the water charged with fine particles is pumped out continuously. The procedure is repeated by increasing the speed of surging till clear water comes out. 3. Development by Compressed Air. In this method, the development is done with the help of an air compressor, a discharge pipe and an air pipe. The air pipe is put into the discharge pipe and is lowered into the well tube, till the assembly reaches near the bottom of the strainer-pipe section. The lower end of the air pipe is kept emerging out of the discharge pipe by a small length. The air entry to the air pipe is first closed and the compressor is then started till a pressure of 6 to 10 kg/cm? is built up. The air is then suddenly made to enter the pipe, at this pressure, with the help of suitable quick-opening valve. This sudden entry of air into well creates a powerful surge within the well causing loosening of fine material surrounding the perforations. When the pressure decreases, water enters the well bringing the loosened particles with it. The continuous air injection creates an air lift pump, and the water carrying fine particles is pumped out. The process is repeated till clear water comes. The pipe assembly is then lifted up, and the surging is again created. The operation is repeated at intervals along the screen section till the well is fully developed, 4, Development by Back Washing In this method, in addition io the compressor, a discharge pipe and an air pipe, and additional small air pipe is used. The well is sealed at its top so that is becomes air-tight. The discharge pipe and air pipe assembly is lowered in the well, as in the previous method, but the end of the air pipe is kept inside the discharge pipe. A small air pipe is fitted at the top of the air-tight cover and is provided with a three-way cock. With the help of the three-way cock, air can be admitted to the well either through the long air pipe (but inside the discharge pipe) or through the long air pipe fitted at the top. Air is first made to enter the long air pipe. This forces air and water out of the well through the discharge pipe. When clear water comes the valve is closed, and water level is allowed to increase in the well. The valve is then turned to the other side so that air enters through the discharge pipe and at the same time agitates the fine particles surrounding the well. Calgon is often added to water. When air starts escaping fromGROUND WATER : WELLS 9 the discharge’ pipe, the valve is turned so that air enters the long air pipe, and the assembly works as an air-lift pump and the water is pumped out. The procedure is repeated till clear water comes and the well is fully developed. 5. Development by dry ice (solid sodium dioxide) In this method, well is developed with the help of two chemi- cals : hydrochloric acid and solid sodium dioxide (known as dry ice). First of all, hydrochloric acid is poured into the well. The well is capped at the top and compressed air is forced into the well. The pressure of the compressed air forces the chemical into the formation. The cap is then removed and blocks of dry ice are dropped into the well. The sublimation releases gaseous carbon dioxide, and a high pressure of this gas is built up in the well. On releasing the pressure the muddy water is forced up in the form of a jet and is automatically thrown out of the well. Explosion of mud and water extending 40 metres into the air from a well in Utah (U.S.A) was observed when the well was developed with dry ice. 4.14, OPEN WELLS As stated earlier, an open well is essentially of a bigger diameter than of a tube well, and derives its water only from one pervious stratum. Since a tube well, in general, may derive water from more than one aquifer formation, it has greater depth than an open well. The economically feasible depth of an open weil is limited to 30 metres below the ground surface. In a lined open well, the entry of water is from the bottom and not from the sides. An open well is classified as : (i) Shallow well. (ii) Deep well. “wernt | PERVIOUS FORMATION LL Wh wel (0) SHALLOW WELL ae (bd VELL” -PERVIOUS FORMATION FIG. 4.23. SHALLOW AND DEEP WELLS100 WATER SUPPLY ENGINEERING The nomenclature of shallow and deep well has nothing to do with the actual depth of the well. A deep well is a well which is supported on a mota layer and draws its water supply, through a hole bored in it, from the pervious formation below the mota layer. A shallow weil, on the other end, penetrates the pervious Stratum only and draws its water supply through it. The term mota layer also sometimes known as matbarwa or nagasan, refers to a layer of clav, cemented sand, kankar or any other hard material. The mota layer gives structural support to the open well, and is found throughout the Indo-Gangetic plain. These mota layers may either be continuous, or may be localised and may be found in different thicknesses and depths at different places. PERVIOUS STRATUM FIG. 4.24. DEEP WELL ON LOCALISED MOTA LAYER Fig. 4.23 (a) shows a shallow well which derives water from the pervious stratum, and does not rest on a mota layer. Fig. 4.23 (b) shows a deep well resting on a continuous mota layer. Fig. 4.24 shows a deep-well resting on a localised mota layer and deriving its water from the second pervious stratum. Actually, a shallow well can be deeper than a deep well. However, since a shallow well draws water from the first pervious stratum (ie. top formation), the water in it is liable to be contaminated by rain water percolating in the vicinity, and may take with it mineral organic matter such as decom- posing animals and plants. The water in a deep well is not liable to get such impurities and infections. Also, the pervious formation below a mota layer normally has greater water content and specific yield. Hence discharge from a deep well is generally more than a shallow well. The open well may further be classified as : (i) Kachha well or unlined well. (ii) Well with impervious lining. , (di) Well with pervious lining.GROUND WATER : WELLS 101 Kachha well. A kachha well is a temporary well of a very shallow depth. It is suitable only in hard formations the walls of which can stand vertically. They are suitable only when the water table is very near the ground surface. Such weils often collapse after some time, and are dangerous. Well with impervious or pucca lining. This is the most common type of open well, and is suitable for all types of formations. Once constructed, it becomes a permanent source of water supply. Im- pervious lining for an open well in sandy formations is most essential to gives structural stability to the well. (a) SHALLOW WELL WITH (b) DEEP WELL WITH PUCCA PUCCA LINING LINING FIG. 4.25. WELLS WITH PUCCA LINING The thickness of impervious lining (steining) varies from 30 to 60 cm and may be either in brick masonry or in stone masonry. The linings carry well curbs under them. Well curbs may be constructed of either wood, iron or reinforced concrete. In a pucca well, the flow is not radial. Water enters only from the bottom and, after a virtual cavity has been formed at the bottom, the flow is spherical. [STEINING ATER TABLE BALLAST FIG. 4.26. WELL WITH PERVIOUS LINING.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.GROUND WATER : WELLS 103 The formula for discharge, in cumecs, from an open well with impervious lining may be written as : Q=Axv or Q=AxCXh cumecs (4.20) where Q =discharge, in cubic metres second A =cross-sectional area of flow into the well as its base, in m°* v = mean velocity of water percolating into the well, in metres/sec A = depression head in metres C = percolation intensity coefficient. This is a constant of the formation around the well. Its value is greater for coarser soil and smaller for finer soils. (m/sec under unit. head) The above formula can also be derived from Darcy’s law as under : », Q=kAIH=kA t= or Q=C.Ah w=-(4.20) Due to cavity formation, the area A is taken to be equal to : times the actual cross-sectional area of the bottom of the well. , From the above expression, it is clear that the discharge increases with the percolation head h. However, the percolation head cannot be increased beyond a certain critical value because otherwise the percolation velocity will be exceeded and the soil particles will be disturbed and dislodged. The critical value of A at which the velocity is critical is known as the critical depression head. Normally, the depression head is kept equal to t of the critical head ; such a head is known as the working head. Maximum yield or critical yield therefore will be obtained cor- responding to the critical depression head. The yield under the working head is known as the maximum safe yield. From a pumping test, therefore, we can find the maximum safe yield. 2. Recuperation Test Though the constant level pumping gives an accurate value of the safe yield of an open well, it is sometimes very difficult to regulate the pump in such a way that constant level is maintained in the well. In such circumstance, a recuperation test is resorted to. In the recuperation test, water level is depressed to any level below the normal level and the pumping is stopped. The time taken for the water to recuperate to the normal leve} is noted. From104 WATER SUPPLY ENGINEERING the data, the discharge from the well can be calculated as under (Fig. 4.28) : Let aa = Static water level in the well, before the pum- ping started bb = water level in the well when the pumping stopped Ay = depression headin the well when the pumping stopped (metes) cc = water level in the well at a time 7 after the pumping stopped = depression head in the well at a time 7 after the pumping stopped (metres) h =depression head in the well at a time ¢ after the pumping stopped (metres) dh = decrease in depression head in a time dr t,T =times in hours. Thus, in a times ¢, reckoned from the instant of stopping the pump, the water level recuperates by (4, — h) metres. In a time dt after this, the head recuperates by a value dh metres. . Volume of water entering the well, when the head recuperates by dh is dV =adh we) where A =cross-sectional area of well at its bottom. Again, if Q is the rate of discharge in the well at the time t, under the depression head A, the volume of water entering the well in a time d¢ hours is given by dV =Q.dt GROUND LEVEL FIG. 4.28. RECUPERATION TESTGROUND WATER : WELLS 105 But Quh or Qz=Kh +«(2) “ dV = Khdt -»(3) where K is a constant depending upon the soil at the base of the well through which water enters. Equating (1) and (3), we get Khdt =— Adh (4) The minus sign indicates that A decreases as time 1 increases. Integrating the above between the limits : =0 when h=h, t=T when h=h2 T Ay K dh we get al dt =— f = AJ, ny ft T Ay £{ f dh or = dt= =— AJ, hg From which K AT = [Ween ji K Mog ft. 2308 logue Mt wn(4.21) 2 AT Oe RT Thus knowing the value of Ay, 42 and 7 from a recuperation test, the quantity K/A can be calculated. K/A is known as the specific yield or specific capacity of an open well, in cubic metres per hour per sq. metre of the area through which water percolates under one metre depression head. In the absence of the recuperation test, the following rough values of K/A specified by Marriot can be adopted. TABLE 4.2. x A unit de Type of soit Cubic metres per hour, sq. metre of area under lepression head Clay 0.25 Fine sand 0s Coarse sand 1.00 Knowing the value of KAA by observation, the discharge Q from a well under a constant depression head H can be calculated as under : Q=KH (from 2)aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.WATER SUPPLY ENGINEERING ILLUSTRATIVE EXAMPLES Example 4.1. Design an open well in fine sand to give a discharge of 0.003 cumecs when worked under a depression head of 2.5 metres. Solution : Required discharge Q = 0.003 cumecs = 0.003 x 3600 = 10.8 m’/hour From Eq. 4.22, _(K o= (Saw (0) For fine sand, x = 0.5 m’/hour per m* of area, under unit depression head H = depression head =2.5 m Substituting values in (1), we get 10.8 = 0.5 x A x 25 A= 108 mn? = 8.64 m?. ~ Osx 25 ~. Welldiameter d = V a4. V 4X 864 337 m, a a (say 3.4 m) Alternative Solution Another method to find the well diameter is to use the discharge formula (Eq. 4.20) in terms of percolation coefficient. From Eq. 4.20, Q=C.A.H. (2) From Table 4.2, the percolation or permeability constant for fine sand can be taken equal to 0.0075 cm/sec (average). C = 0.0075 cm/sec = 7.5 x 107° m/sec Q = 0.003 = 3 x 10° m’/sec H=25 m A= percolation area O_. 8x10" Lig? A= ==, ~ = lom CH 75x 10° x 2.5 If no cavity is formed at the bottom, A =5¢ 2 If full hemispherical cavity is formed, A =aGROUND WATER : WELLS 109 Usually the area of cavity is between the two values. =i (ta at) =3 ted ag? A =5 af + 27) = ad’ waa Thus, the area of percolation at the well bottom may be taken equal to + times the cross-sectional area of well bottom Example: 4.2. During a recuperation test, the water in an open well was depressed, by pumping, by 2.5 metres and it recuperated 1.8 metres in 80 minutes. Find (a) yield from a well of 4 m diameter under a depression head of 3 metres, (b) the diameter of the well to yield 8 litres/second under a depression head of 2 metres. Solution : From Eq. 4.21, the specific yield is given by K _ 2303 1, M1 AT eh, a —80_4 ‘where T =time in hours =e73 hours Ay=2.5 m hy =2.5-18=0.7 m K _2303x3, 25 _ Ft PE hosw 5s = 0.955 (a) Yield from the well of diameter 4 m : A= 3 (4)? = 12.56 m? K Q=(4)4" = 0,955 x 12.56 x 3 = 36 m'/hour = 10 lit/sec. (b) Yield= 8 lit/sec = 28.8 m’/hour (since 1 litsec= 3.6 m’/hour) o= (Fan.110 WATER SUPPLY ENGINEERING =2, (4) = 238, _1 A(R) AS * D8 = 15.05 m? d = 437m = 4.4m (say). Example 4.3, 4 tube well of 30 cm diameter penetrates fully in an artesian aquifer. The strainer length is 15 m. Calculate the yield from the well under a drawdown of 3 m. The aquifer consists of sand of effective size of 02 mm having coefficient of permeability equal to 50 miday. Assume radius of drawdown equal to 150 metres. Solution : From Eq. 4.6 c, the discharge is given by 2.72 bks Q- Rk logue Here 6 =thickness of aquifer length of strainer = 15 m drawdown = 3 m k = coefficient of permeability= 50 m/day R=150 m r=1Scem=0.15m g=22% 15 x 50x 3 m’/day logu F748 = 2040 m'/day = 85 m’/hour = 23.6 lit/sec. Example 4,4. A tube well penetrates fully an unconfined aquifer. Calculate the discharge from the tube well under the following conditions: Diameter of the well =30cm Drawdown =2m Effective length of the strainer under the above drawdown =10m Coefficient of permeability of aquifer = 0.05 cm/sec Radius of zero drawdown = 300m Seeaa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.112 WATER SUPPLY ENGINEERING Lope = 2:72 x 30 X 5 X60 _ 9 54 7 ~ 3600 x 24 x 0.08 R vast ; __R_ _ 300 "= 34g = Jagr = 0.0862 m Hence adopt well of 9 cm diameter. Example 4.6, An artesian tube well has a diameter of 20 cm. The thickness of aquifer is 30 m and its permeability is 36 miday. Find its yield under a drawdown of 4 m at the well face. Use radius of influence as recommended by Sichardt. Solution : From Eq. 46 c, we have 72 bk Q= 2.72 = logio Here b6=30 m _ ___36 k = 36 m/day ( = Tce s=4m r=0.10 m R= 3000s Vk, from Sichardt formula = 3000 * 4 575 3600 = 2.72 x 30 x 36x 4 245 logo oT = 3470 m'/day = 144.5 m’/hour = 40.2 lit/sec (or 0.0402 cumecs). Example 4.7. A well penetrates fully a 10 m thick water bearing stratum of medium sand having coefficient of permeability of 0.005 misec. The well radius is 10 cm and is to be worked under a drawdown of 4 m at the well face. Calculate the discharge from the well. What will be the percentage increase in the discharge if the radius of the well is doubled ? Take R=300 mi in each case. 245 m. Q=aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.lo WATER SUPPLY ENGINEERING When both the wells are aXcharging, the discharge from each well is given by Eq. 4.14 : 1 = Qs = BtKbLH = hy _ 2.72 kbs RR loge 5B login 7B _ 2.72 X 60 X12 X 3 _ 2.72 x 60 X 12 x3 1 250 x 250) 3.796 loge (Tc i00 | = 1545 m'/day = 64.4 m’/hour . % decrease in the discharge _ 72.0 - 64.4 ee =—T0 x 100 = 10.55% Example 4.10, A gravity well has a diameter of 60 cm. The depth of water in the well is 40 metres before pumping is started. When pumping is being done at the rate of 2000 litres per minute, the drawdown in a well 10 metres away is 4 metres and in another well 20 metres away is 2 metres. Determine (a) radius of zero drawdown (b) coefficient of permeability (c) drawdown in the well (d) specific capacity of the well (e) maximum rate at which water can be pumped from the well. Solution : (a) For a tube well in unconfined aquifer, we have from Eq. 44 b = 136k (H =k’) Q ~R logio > ‘Here, wesfave H=40; At r=10m,h=40-4=36m es At r=20m,A = 40-2 = 38m. i Applying the above equation at these two locations, we have 40° 40 - = togw logi £ or tog = = mn togn-& = 05132 login $132, or loge = tog ( " " R or 20 RISEGROUND WATER: WELLS 17 J a R = (6.1352) T3808 = (6.1352)? R=4152m (b) Q = 2000 litres/min. =2m/min. (since 1 litre/min. = 0.001 m’/min.) R=41.52m;H = 40m, h=36m, 10 m = = 136k (40° - 36°) Q=2 Top 452 08m Ta _ 2 52 1.36 (40° — 36°) tog is = 0,003 m/min. = 431 m/day. (c) Depth of water in the well is given by 9 1.36 x 0.003 (40° — Ha) 4152 lB 30° 2 2 41.52 1600 — He = 35 5co003 * 8930 = 1049.58 Ay = 23.46 m. Hence drawdown at the well = 40 — 23.46 = 16.54m (d) Specific capacity is defined as the discharge per unit draw- down. Let it be designated by S,. It is not constant, but decreases as the discharge increases (sce §4.6). Let us assume that the yicld is directly proportional to the drawdown or to the radius of zero- drawdown. QoR or Q=C.R where C is a constant. For a given data, C= DIS 2 “77 0.04817.18 WATER SUPPLY ENGINEERING: =2-_2_; R C= 004817 in general. Now corresponding to. drawdown of 1 m, discharge QO = S.. Hence radius of zero drawdown —Se__ Se ~C 0.04817 Hence O=5S.= 1,36 .k (40° — 39°) logio * — 1.36 x 0,003 (40° — 39°) loge (que x03} or Se login (69.2 S-) = 0.3223. Solving this by trial and error, we get Se = 0.258 m*/min. Hence, specific capacity of the well is 0.258 m?/min/m depression head. (e) maximunr rate of discharge Q,, will be obtained when draw- down in the well is equal to H, ie., when Ho = zero. On = 1:36. 0.003 (40° = 0°) lo 9, 8" N04B1T x 03 or Qn loge 69.2 Qm = 6.528 Solving this by trial and error, we get Qn = 2.85 m’/min, 4.18. UNSTEADY FLOW The analysis of flow towards wells discussed in the previous articles is based on the assumption that steady state of flow is developed immediately after pumping is started. Actually, the cone of depression fluctuates with time. The gradual approach of cone of depression towards a steady state is produced primarily by the removal of water from storage as cone deepens. Hence a storage co-efficient comes into play. The storage co-efficient is a dimensionless constant of the aquifer and may be interpreted as the amount of water in storage released from storage from a column of aquifer of unit cross-section under a unit decline of head. Equations developed for unsteady or transient well flow nor- mally show how the drawdown s of the piezometric surface or water table is related to the time of pumping the well. In Fig. 4.31,GROUND WATER : WELLS 119 FIG. 4.31. TRANSIENT FLOW consider an annular cylinder of thickness dr and radius r. Due to unsteady flow conditions, water will be released from storage of this elementary cylinder. According to definition of storage co-efficient iv 8 . 5 S, the rate = at which a certain volume V is released from storage over an aquifer of area A is given by aV __ oh ar ~~ at 4 =) where V=volume of water released per horizontal area A of aquifer. =height of piezometric surface or water table above lower boundary of aquifer. S = storage co-efficient. A =area of the aquifer to which x applies. t= time. Since h decreases with time ¢, minus sign with ah/dar has been used. For the elementary cylinder of the aquifer, A = 2xr dr. Hence av ah a a dards. (2) Let Q, = discharge entering the outer face of the cylinder. Q2 = discharge leaving the inner face of the cylinder. . Change in discharge 6q = Q: - Qo.120 WATER SUPPLY ENGINEERING Since the rate of increase in q can be expressed as — a > the increase in discharge over the annular area =— Sar. Substituting this for ar in (2), we get ~ 4dr a ~2nrdy gs .QG) or at For confined radial flow, we get from Darcy law, q =2ar re 4 aa72 * a rey =2nT Bae g (4) Substituting in (3), we hi ah oh _ ah wrt roa] = 2.5, which simplifies to ah , 10h _ Sah tre Tha eh) This is the basic equation for unsteady flow towards the well. Theis (1935) obtained a solution for this equation based on the analogy between ground water flow and heat conduction, by assuming that the well is replaced by mathematical sink of constant strength such that h = H before pumping begins and that h>H as ro after pumping begins (¢ 2'0). The solution is P< _ = 2 * we(4.25 Aol san ee = 2. or sa EV w we(4.25) where Wu) =f du = well function. Eq. 4.25 is known as the non-equilibrium equation ot Theis equation. The integral in the above equation is a function of the lower limit, and is known as exponential integral. It can be expressed as a convergent series so that Eq. 4.25 can also be expressed as 3 = 2 [- oy we 3 asp 0.5772 — logeu +u — Tat +a ar re (4.25. b)121 LLS ER : WEL GROUND WATI $710000°0 £4£0000'0 9110000 09£000°0 SPT 1000 6LL€00°0 SOELO'O 168P0°0 r6Iz0 6tL'8 9888 066'8 reo OES Oss6 L886 1701 ror 5 O1XN GorxN =") (9) NOMONAA TIAM dO SANIVA ‘t+ ATEVL :122 WATER SUPPLY ENGINEERING Wenzel tabulated the values of W(u) for various values of u ranging from 10-" to 9.9. Table 4.3 gives the values of W (u) for u ranging from 107“ to 9. From the table, when u=5, W(u) = 0.001148 and when u=5x1073, Wu) = 4.726. The values of formation constants S and T can be found by measuring drawdowns in observation wells when the well under study is pumped at a constant rate of discharge Q. There are several methods of determining S and T, but we will discuss here following three methods : (a) Theis method, (6) Jacob’s method, (c) Chow's method. (2) THEIS METHOD Theis proposed a curve-fitting method for finding formation constants S and T from a pump out test. From Eq. 4.25, we observe that s=[& |¥@ or log W(u) = [ioe 457 1] + logs w(4.26 a) r_ aT _ 5 P and = [+ lu or logu = [8 + log — (4.26 6) If a constant withdrawal rate (Q) is maintained, the bracketed portions of the above two equations are constant for a given pumping test. It is to be noted that s is related to 7/t in a manner that is similar to the relation of W(u) to u. Hence if a plot or data curve is made between s and r’/t on logarithmic co-ordinates tracing paper (Fig. 4.32 a) to the same scale as the type curve W(u) versus u (Fig. 4.32 b), the data curve will be similar to the type curve. Procedure < (i) In the observation well situated at a radial distance r from the main well, observe s and f¢. (ii) Plot s versus/’/¢ on a log-log tracing paper (Fig. 4.25 a). (iii) Plot Wu) versus u on log-log graph ‘paper (Fig. 4.32 b). (iv) Keep Fig. 4.32 a on Fig. 4.32 6, and adjust it in such a way that when the co-ordinate axes are held parallel, the dataGROUND WATER: WELLS rm) 109 2/1 me/pay 108 (a) DATA CURVE 6' (c) CURVE FITTING FIG. 432, THEIS METHOD.124 WATER SUPPLY ENGINEERING curve is oriented in a position which represents the best fit of the field data to the type curve. (v) With both graph sheets at the best match position, an arbitrary point P on the top curve is selected and pricked through. (vi) The co-ordinates (a, 6) and (a),6;) of the match point are noted from both the curves. Thus’ the pair of values [s, #(u)] and [?°/1,u] are known. The aquifer constants are then calculated from the relations : -2y z TF as (u) w(4.27 a) and gn eT A427 b) ra (6) JACOB’S METHOD Jacob suggested a method which completely avoids curve fitting. He observed that when r is small and ¢ is large, u may be small and hence all terms after 2nd term of the serics expansion (Eq. 4.25 b) of W(u) may be neglected. Thus W(u) =— 0.5772 — logeu eo 2uje es s=3* Fl 0.5772 — loge u} Q 47t or S= a loge ay — 0.5772 w(4.28) For the same observation well, if 5; and sz are the observed drawdown at times ¢ and % since pumping started, we have As =5:-5) _ 23030, = Far loaw? (4.29) If a plot is made between s and logit (Fig. 4.33) then for, one log cycle of time difference (ie. tf = 10%), we get — 2.3030 Ase nT _ 2.3039 or T= as w=-(4.30) Extrapolating the straight line of the curve to intersect with the zero drawdown axis permits the calculation for S. Let ft beaa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.GROUND WATER : WELLS , 127 4, Draw the tangent to the curve at the chosen point P and determine the drawdown difference As per log cycle of time. 5. Compute the function F(u) by the relation aS - FW) =55 +» (4.33) 6. Knowing F(u) and using Fig.+4.34, find u and W(u). 7. Compute S and T from the following relations : el T ae Wu) and gah te Note. For small values of u, we have from Jacob’s method: ay = 23030 4nT = 2g (when f= 10%) Also, s= & Mu) _ = ¥@) Flu) = se 7303 (4.32. a) For F(u) <2, the above equation can safely be used. For Fu) > 2,u becomes large. Hence Eq. 4.32 should be used. Example 4.11. Theis Method. A weil fully penetrating a confined aquifer is pumped at a uniform rate of 2500 litres per minute. The drawdowns in an observation well situated at 60 m away are given in Table 4.4. Using Theis method, determine the formation constants of the aquifer (Adapted from data from U.S. Geological Survey). logw 2 TABLE 4.4.2K SUPPLY ENGINEERING WATE 128 Solution Table 4.5. in and r/t are tabuted The values of 4, 5 OL x 97 Ol Lez Ol x 887 OLX oe sOLX 2er OLX srs OLX 879 OL x $98 OLX t0°1 OLX OET OLX eet OLX ONT OLX 8877 1-01 29° 1-01 x OFT (01 S71 1-01 x FO"! z OL x £88 7-01 F6'9 7-01 98's z-O1X Lt z-OlX Le 7-01 827 7-01 807 p01 XL 201% S71 OLX Ove OLX Cr OL x srs sol x sro OLX P98 OL X $0" Ol x OFT OlX elt Ol X 207 Ol X 657 Ol x 9F'€ OLX SUS = OLX 716 01 £69 01 X 169 ¢ -O1 x 96'S OE x LIP 01x LPE OLX 827 01 x 807 e-OTX fei 01 X 661 01x HOT p01 x 69 ( dopa} YA sop 1 oud (Sopa) (a1 99 = 4) AAWND VLVG AOA SNOLLVLAdWOD sb AVLGROUND WATER: WELLS 129 A plot is made between s and r’/t as shown in Fig. 432 (a) on a log-log tracing paper. The type curve [W(u) versus u] is shown in Fig. 4.32 (6), prepared from data of Table 4.3. The data curve of Fig. 4.32 (a) is superimposed on the type curve and properly oriented to get the best possible fit. A match point P is pricked (Fig. 4.32 c) and its co-ordinates are found as follows : s=052m; Ww)=2.96 Fa7x10 ; u=3x 10? Discharge Q= 2500 litres/min.= 2.5 m’/min. = 3600 m’/day a. a T= gas VO) = Fux ose * 2% = 1631 m’/day/m 2 and g = MT LA X3X WW > 1631 = 0.00028 r/t 7x 10° Example 4.12 Jacob’s Method. Solve example 4.11 by Jacob's method. Solution: Fig. 4.33 shows the plot between s and ¢. Most of the points lie on a straight line. The drawdown As for one log cycle of time difference comes out to be 0.38 m. Hence from Eq. 4.30, 7 = 2303Q _ 2.303 x 3600 4nAs 4xx 03 = 1736 m*/day/m. Extending the straight line so as to cut the time axis, we get to = 2.4 x 10°“ days. g = 2:25Tto _ 2.25 x 1736 x 2.4 x 107* r (60) = 0.00026 Example 4.13. Chow’s Method. Solve example 4.11 by Chow's method. Solution : The plot between s and ¢ is shown in Fig. 4.35. Choose any point P whose co-ordinates are s = 0.45 m and ¢ = 3.47 x 107* day.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.132 WATER SUPPLY ENGINEERING " FAULT SPRING .° / PERMEABLE FIG. 4.38 FAULT SPRING 4.37). If this cover is locally broken by fracturing or if the artesian aquifer outcrops, the artesian water below emerges as an artesian spring. Artesian spring, also known as Geysers, are of infrequent occurrence. The deep-seated springs are associated with vulcanicity and deep fractures, and yield juvenile water and not the rainwater. Fig. 4.39 shows two methods of collecting water from springs. DIVERSION DITCH (b) FIG. 439. COLLECTION OF WATER FROM SPRINGS *GROUND WATER : WELLS 133 Infiltration Galleries It is a small tunnel in the form of pipes laid under the ground to tap up underground flow available at moderate depth. These tunnels could be of wood, stone or bricks. Their shape is generally INFILTRATION GALLERY FIG, 440. INFILTRATION GALLERY circular, and they are covered by graded filters all around. The ground water can enter the tunnel through side and bottom. These galleries are often constructed parallel to a river bank to collect the inflow of water to river. Fig. 4.40 shows a typical infiltration gallery sur- rounded by a three layer graded filter consisting of : () 16 cm ballast (25 mm to 50 mm le) around the pipe which has perforations. (ii) 16 cm large pebbles (12 mm to 24 mm) as intermediate layer. (iii) 24 cm fine pebbles (3 mm to 10 mm size) as the outer layer. Flow into Infiltration Gallery The analysis of flow towards an infiltration gallery running parallel to a stream etc: can be done on the basis of following assumptions proposed by Dupuit : 1. Soil is isotropic, homogeneous and incompressible. 2. The tangent of the angle of inclination of the water table, ie. its slope is equal to its sine, and 3. The flow is uniform and horizontal throughout the depth of aquifer. Consider an infiltration gallery at a distance L from the source. Let H be the height of saturated zone at distance L and H, be the depth of water in the gallery. At any point P distant x from the face, the discharge q passing through the vertical section, per unit length of the gallery is given by Darcy law :134 . WATER SUPPLY ENGINEERING FIG. 4.41. FLOW TOWARDS GALLERY qz=k a (hx 1) (4.32) L H q f dx =«f dh o Ho 2 2 qake a (433) If however, the gallery receives discharge from both the sides, the above discharge will be doubled. Eq. 4.32 traces a parabolic water table which departs significantly from the actual water table shown by dotted line. Example 4,14, An infiltration gallery is situated at a distance of 15 m from a diffusion ditch which penetrates fully the pervious formation of depth 6 m. If the depth of the water in the infiltration gallery is 2m above the bottom of the formation, compute the discharge per metre of the gallery. Take k = 0.5 cm/sec. Solution : k& =0.5 cm/sec = 0.005 m/sec. L=15m H=6m H=2m _ ,-H_ 6-2 q =k = 0.005 35 = 0.00533 m'/sec = 460.8 m’/day/mGROUND WATER : WELLS 135 KAREZ A karez is an underground tunnel driven into the hill-side to tap water from the underground springs. The tunnel has certain bed inclination. Water from the karez is taken in an open channel. KAREZ SHAI fS SHAFTS FIG. 4.42, KAREZ Such tunnels are in use in Baluchistan and North West Frontier Province (West Pakistan). 4.20. RADIAL COLLECTOR WELLS Radial collector wells or horizontal wells are becoming very popular these days. The system consists of a vertical central cylinder of monolithic concrete of about 5 m in diameter which is sunk into the aquifer by excavating the inside earth material. When the desired level is reached, it is sealed at its bottom with a thick concrete plug. The concreted cylinder has precast ports at its bottom end. Through these ports, a number of radial collectors, 15 to 20 cm in diameters are jacked horizontally into the water bearing formations. These form radial pattern of horizontal pipes as shown in Fig. 4.43. Perforated pipes with proper screens are later inserted in these horizontal holes. The length of radial collector may be upto 60 m. Patents for this type of well were obtained by L. Ranney (for Ranney Method Water supplies Inc. Columbus, Ohio) and H. Fehimann (for Grundwasserbauten A.G. Berne, Switzerland). In the Ranney well, slotted pipe is placed directly in the collector hole. In the Fehlmann well, a blank pipe is installed first, and then the perforated pipe is placed inside and the blank casing pipe is removed. During the development of the well, fines are removed and natural gravel packs are formed around the collector wells. The inner end of each collector well is fitted with a sluice valve which can be operated from the pump house above. Collector wells extract relatively large supplies of groundwater from valley fills and other alluvial deposits of high permeability and ample rate of recharge. The entry velocity is very low. Hence it prevents the danger of clogging and incrustation duc to carbonate136 WATER SUPPLY ENGINEERING PUMPING TOWER DEEP WELL PUMPS. HIGH WATER LEVEL CAISSON SEALED AT BOTTOM * | WATER PATH *, + ‘o-b-c-d-e SCREEN PIPE 200-300 LONG, EACH FIG. 4.43. RANNEY’S RADIAL COLLECTOR WELL deposition. The water obtained by this method is clean, fresh and biologically pure. It normally docs not require any treatment. TheGROUND WATER: WELLS 137 initial cost of a collector well exceeds that of a vertical well, but the advantages of large yields, reduced pumping heads and low main- tenances costs offset the initial cost. PROBLEMS 1. Define the following terms : Aquifer, aquiclude, specific yield ; piezometric surface ; water table; perched uquifer. 2. Show, with the help of sketches, various types of wells. 3. Explain the terms ‘storage coefficient’ and ‘coefficient of trans- missibility’. 4. State and discuss assumptions and limitations of Dupuit’s theory. 5. Derive an expression for discharge from a well in an unconfined aquifer. ‘The well fully penetrates it. 6. Derive an expression for discharge from 4 well fully penetrating a confined aquifer. 7. Explain the method determining the coefficient of transmissibility of a confined aquifer by pumping out test. How can this method be extended for unconfined aquifer ? 8. Write notes on the following : (#). well loss (ii) specific capacity of well (ti) spherical flow in well (iv) interference among wells. 9. Describe various types of tube wells. 10. Describe, with the help of sketches, some of the common types of strainers used in tube wells. 11. Explain the Percussion method of drilling a tube well. 12. What do you understand by well shrouding ? 13. Describe in brief various methods of developing a tube well. 14. What do you understand by recuperation test ? Derive the equations used in the test. 15. Distinguish clearly between a shallow well and 2 deep well. How does a deep well differ from a tube well in confined aquifer ? 16. The following observations were recorded during a pumping out test on a tube well penetrating fully in a free aquifer : Well diameter : 25 cm Discharge from the well : 300 m'/hour138 WATER SUPPLY ENGINEERING R.L. of original water surface, before pumping started = 122.0 m. R.L. of water in the well at constant pumping = 171.1 m RL. of water in the observation well = 121.3 m. RLL. of impervious layer = 92.0 m Radial distance of observation well from the tube well = 50 m Determine : (a) the field permeability coefficient of the free aquifer, and (b) radius of zero drawdown. [Ans. (2) 60.7 m/day (6) 157 mj 17. Design a tube well for the following data : (i) Yield required = 0.2 cumec (ii) Thickness of confined aquifer = 40 m (iii) Radius of circle of influence = 300 m (iv) Permeability coefficient = 80 m/day (v) Drawdown =6 m [Ans. 28 cm, or say 30 cm] 18. During a recuperation test, the water in an open well was depressed by pumping by 2 m and it recuperated 1.5 m in 1 hour. Estimate the yield from a well of 2 m diameter under a depression head of 2 m situated in the same area. Derive the expression your use. [Ans. 8.7. m*/hour| 19. A tube well penetrates fully a 8 m thick water bearing stratum (confined) of medium sand having coefficient of permeability of 0.004 m/sec. The well radius is 15 cm and is to be worked under a drawdown of 3 m at the well face. Calculate the discharge from the well. What will be percentage increase in the discharge if the radius of the well is doubled ? Take radius of zero drawdown equal to 400m in each case. [Ans. (i) 275 m’/hour (ii) 9.6%] 20. Design an open well in fine sand to give a discharge of 0.005 cumecs when worked under a depression head of 3 metres. Take the value of the specific yield for fine sand as 0.5 m’/hour per square metre of area, under unit depression head. [Ans, Dia. 3.9 mj3 Water Demand and Quantity 5.L. INTRODUCTION Before designing a proper water works project, it is essential to determine the quantity of water that is required daily. This involves the determination of the following items. 1. Population determination. Determination of population is one of the most important factors in the planning, if the project has to serve the community for a certain design period. Normally, a design period of 20 to 40 years is selected. What will be the population at the end of the design period, is the basic question. This can be achieved by using various methods for population forecast. 2. Rate of demand. The water consumption in a city may be conveniently divided into the following categories : (i) domestic (ii) trade (ii) agricultural (iv) public and (v) losses. The total con- sumption of water depends upon several factors, such as climatic condition, cost of water, living standards of the inhabitants, pressure in the pipelines, type of supply etc. The total quantity of water required divided by the total population gives per capita water demand. The accurate measurement of consumption is often very difficult because standards of supply and maintenance vary widely. 5.2, DESIGN PERIOD Generally, water supply projects are designed for a design period of 20 to 40 years, after their completion. The time lay between the design and completion should not be more than 2 years. In some specific components of the project, the design period may be modified. Different segments of water treatment and distribution sys- (139)140 WATER SUPPLY ENGINEERING tems may be approximately designed for differing periods of time using differing capacity criteria, so that expenditure far ahead of utility is avoided. Table 5.1 gives the design periods far various com- ponents of a water supply project. TABLE 5.1 DESIGN PERIODS FOR PROJECT COMPONENTS Component Design period (ears) Storage by dams 50 Infiltration works Pump sets (All prime movers except electric motors {i) Electric motors and pumps Water treatment units Pipe connections to the several treatment units and other small appurtenances Raw water and clear water conveying mains Clear water reservoirs at the head works, balancing tanks and service reservoirs (over head or ground level) Distribution system 8.3. POPULATION FORECAST The data about the present population of a city under question can always be obtained from the records of the municipality or civic body. However, a water supply project is designed to cater the needs of the community upto the end the design period which may extend upto 2 to 4 decades, before the project is abandoned or enlarged by reason of inadequacy. There are several methods for population forecast, but the judgment must be exercised by the engineer as to which method is most applicable for a particular location. The increase in population of city depends upon several factors such as living conditions of the city and its environs, industrial potential, state of development, location with respect to road and rail links, climatic conditions etc. The entire population of a city may not be evenly distributed, due to variations in the land use pattern and available facilities etc. The population density, indicating the number of persons per unit area, and the distribution of population should also be studied for efficient design of the distribution system. Following are some of the important methods of population forecasts or population projections :WATER DEMAND AND QUANTITY 141 . Arithmetical increase method. Geometrical increase method. Incremental increase method. Decreased rate of growth method, . Graphical extension method. . Graphical comparison method. Zoning method or master plan method. . Ratio and correlation method. . Growth composition analysis method. . Arithmetical Increase Method This is the most simple method of population forecast, though it generally gives lower results. In this method, the increase in population from decade to decade is assumed constant. Mathematically, this hypothesis may be expressed as dP ank w(5.1 a) ee a where ap is the rate of change of population and K is a constant. From the census data of past 3 or 4 decades, the increase in population for each decade is found, and from that an average increment is found. For each successive future decade, this average increment is added. The future population P, after » decades is thus given by Pr=P+nl (5.1) where P, = future population at the end of n decades P =present population, J = average increment for a decade. This method should be used for forecasting population of those large cities, which have reached their saturation population. 2. Geometrical Increase Method or Uniform Percentage Growth Method In this method, it is assumed that the percentage increase in population from decade to decade is constant. From the population data of previous three or four decades, the percentage increase in population is found and its average is found. If f, is the average percentage increase per decade, or r, is the increase per decade expressed as ratio, the population P, after n decades is given by142 WATER SUPPLY ENGINEERING Ip yn 1 Py =P(t 63] =P(l +n) wo(5.2) Eq. 5.2 can be derived very easily as under : Let P be the present population and P, be the population after one decade. =p+te pe A" ; Then, Py P+ am? P(.tas | wi) Similarly, population P2 after two decades is Py=P,+ Hep =P, (144): 1+ P= Pi ij\-=P (14:45), w(ié) 100 While the arithmetical average method is analogous to the ‘simple interest method’, this method is analogous to the compulation of income by the ‘compound interest method’. This method gives higher results since the percent increase never remains constant but, instead, decreases when the growth of the city reaches to saturation. " Hence Pap (1+) The value of rz can be found from the expression vn n= (#) -1 (5.2. a) Alternatively, 7, can be determined by computing the average of growth rates of several known decades of the past : 7 = Mctease in population ulation for each decade. original population Knowing ri, r2.....% for each decade, the average value r, can be found either by arithmatic average method or by geometric average method : (i) By arithmatic average method : ntnt. Ty - n 1 w(5.2b) (6) By geometric average method Tes (Melee 1) ue (5.20) The field engineers use the arithmatic average method for computing r, (or J,) since it gives slightly higher (and hence safer)WATER DEMAND AND QUANTITY 143 values. However, the Manual on water supply and treatment recom- mends to use the geometric mean method. 3. Incremental Increase Method This method combines both the arithmetic average method and the geometrical average method. From the census data for the past several decades, the actual increase in each decade is first found. Then the increment in increase for each decade is found. From these, an average increment of the increases (known as incremental increase) is found. The population in the next decade is found by adding to the present population the average increase plus the average in- cremental increase per decade. The process is repeated for the second future decade, and so on. Thus the future population at the end of n decades is given by : P,=P+nlt ner), (53) where P=present population J = average increase per decade r = average incremental increase n=number of decades. Eq. 5.3 can be easily derived as under : Let P be at the present population. The population P; after one decade will be P\=P+Ii+Ir ai) Similarly, population P, after 2 decades is PraPiti+2r=P+21+3r=P + 214224), Population P, after 3 decades is Pra Prt 1+ 3r=P +314 6r=P 43142040, Hence, population P, after n decades is Pp=P+ni+2 20, 4. Decreased Rate of Growth Method or Logistic Method It is found that the rate of increase of population never remains constant, but varies. Fig. 5.1 shows a plot between the population P and the time T for a developing city. The population of a city will grow until it reaches a saturation population which is established by limit of economic opportunity. All populations thus grow according to the logistic or S-curve. The curve ABC (Fig. 5.1 a) starts with144 WATER SUPPLY ENGINEERING a low rate of growth, followed by a high rate and then at a progressively lower rate to the saturation population. Thus in Fig. 5.1 (@) part AB has geometric increase while there is first order increase from B to C. From D to E, near point of inflection, there is straight line increase. The curve abc is the first derivative curve indicating the rate of growth. P, SATURATION POPUL ATION a Zz Q & a 2 9 a A TIME T > (ag, t < a t, a’ e = g i cy TIME T — (b) FIG. 5.1. INCREASE IN POPULATION WITH TIME : LOGISTIC CURVE It is seen that in the part bc of the curve, the rate of increase decreases. Fig 5.1 (b shows the same plot in which the population is plotted on log scale. It is clear that for the part 4,B,, we have increasing rate of growth while for the part B, C,, there is decreasing rate of growth of population. Thus, as the city becomes large, a decreased rate of growth may be expected. This factor should be taken into account while computing future population, as illustrated in Example 5.1.WATER DEMAND AND QUANTITY 145 Logistic curve analysis The logistic curve used in modelling population trends has S-shape, as shown in Fig. 5.1 (a). The Gompertz curve and the logistic curve are both used in establishing long term population trends of large population centres. Both of these curves are S-shaped and have upper and lower asymptotes. According to P.F. Verhulst, the logistic curve can be represented by the equation loge (El — log PoP a KP..t (5.4) where = Ps = saturation population Po = population at starting point A P=population at any time ¢ from origin A. K = constants tope | (AE) x ( Po )] =-KPe P,— Py P,-P Pe cctnghies or =p =p, lee (—KPs.t) Ps —Pi 7 or pit Be * | logs '(— K Pst) P= aoe (5.5) 1+ =p loge! (- K Ps.) Selecting =m and —K.P,=n, where m and n are constants, we get ps——Ps__ 1+ mloge | (nt) If three pairs of characteristic values Po,P:, and P2 at time t=, t= and t = 4%, = 2z, are selected from the useful range of census population data, the values of P;,m and n can be found from the following simultaneous equations : 2 PoPi Pr — Pi (Pot Pi) (5.6) P, PoP? (5.7 a) m= fete (5.7. b) 1 Po(Ps - Ps) n = 7, be [F, (Ph) ww (5.7 ¢) Eq. 5.6 can also atternatively expressed as : P=—Ps_ (5.8) 1+eet146 WATER SUPPLY ENGINEERING Ps, a and b may be determinéd from three successive census populations and the Eqs : = 2 PoP: Pr — Pi (Po + Pr) P; «(5-9 . PyP: PF Goa) a = loge P= Po 1(5.9) Po = iog, Pos= Pi) b= i lon FP (5.90) where n is the time interval between successive censuses. The values of P,, a and b so obtained may be substituted in Eq. 5.8 to estimate the population for any period ¢ beyond the base year corresponding to Po Eq 5.8 in more useful for computation with the help of electronic calculators. See example 5.4 for illustration. 5. Graphical Extension Method In this method, a curve is drawn between the population P and time 7, with the help of census data of previous few decades, so that the shape of the population curve is obtained — upto the present period. The curve is then carefully extended from the present DESIGN POPULATION * 80,000 80; 70} 60} ny oO 3 POPULATION IN THOUSANDS: 193! 194 195! 1961 1971 1981 199% 200! 20) TIME T FIG. 5.2 GRAPHICAL EXTENSION METHOD.WATER DEMAND AND QUANTITY 147 to the future decades. From the extended part of the curve, the population at the end of any future decade is approximately determined. 6. Graphical Comparison Method This method is a variation of the previous method. It assumes that the city under consideration will develop as similar cities developed in the past. The method consist of plotting curves of cities that, one or more decades ago, had reached the present population of the city under consideration. 30 G00 wood | _[ | 70 000} 60 001 50 000 POPUL ATION 000. 1930 1840 1950 1960 1970 1980 1990 2000(A) YEAR 1930 1940 1950 1960 (8) 1925 1935 1945 1958 (Cc) 1935 1945 1955 1965 (D) 1920 1930 1940 1950 (E) FIG. 5.3. GRAPHICAL COMPARISON METHOD Thus, as shown in Fig. 5.3, the population of city A under consideration is plotted upto 1970 at which its population is 62,000. The city B having similar conditions, reached the population of 62000 in 1930 and its curve is plotted from 1930 onwards. Similar curves are plotted for other cities C, D and E which reached the population of 62000 in 1925, 1935 and 1920 respectively. The curve of city A can be then be continued (shown by dotted line), allowing it to be influenced by the rate of growth of the larger cities. In practice however, is is difficult to find identical cities with respect to population growth. 7. Zoning Method or Master Plan Method This is probably a scientific method using the limitations imposed by the town planner in the increase in density of population of various parts of the city. For this, a master plan of the city is prepared, .148 WATER SUPPLY ENGINEERING dividing it into various zones such as industrial, commercial, residential and other zones. Each zone {s allowed to develop as per master plan only. The future population of each zone, when fully developed can be easily found. For example, sector A of a residential zone has 1000 plots. Allowing 5 persons per plot, the population of this sector, when fully developed, will be 1000 x 5= 5000 persons. Similarly, the development of cach zone can be estimated. This method is more advantageous because of the fact that the total water requirement of the city depends not only for domestic purposes, but also for commercial, industrial, social health and other purposes, Population density is generally expressed as number of persons per hectare, and their values may be estimated from data collected on existing areas and from zoning master plans for undeveloped areas. Table 5.2 gives the values of common population densities. TABLE 5.2, COMMON POPULATION DENSITIES Area type 1. Residential - Single family units 2. Residential - multiple family units. 3. Apartments 4. Commerical areas 5. Industrial area 8. Ratio and Correlation Method The population growth of a small town or area is related to big towns or big areas. The increase in population of big cities bear a direct relationship to the population of the whole state or country. In this method, the local to national (or state) population ratio is determined in the previous two to four decades. Depending upon conditions or other factors, even changing ratio may be adopted. These ratios may be used in predicting the future population. This method takes into account the regional and national factors affecting population growth. This method is useful for only those areas whose population growth in the past is fairly consistent with that of state or nation. 9. Growth Composition Analysis Method The change in population of a city is due to three reasons: (@ birth, (i) death, and (iii) migration from villages or other towns. The population forecast may be made by proper analysis of these three factors. The difference between birth rate and death rate gives the natural increase in the population. Thus, P, = P + Natural increase + Migration.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.152 WATER SUPPLY ENGINEERING Py, = 74100 (1 + 38.8 i = 1,38,590. The above computations are based on the value of J; computed by arithmatic average method. If, however, geometric average method is used, as recommended by the Manual, we have Be= (Incl eee In)" = ( 37.50x62.42x 54.85 x 38.55 x 18.26 8.97 ) \“* = 30.54 (against a value of 36.76) », = 74100 (: + 28s) = = 126272 3. Incremental Increase Method P,=P+nr+2@t), (5.3) where, 1 = 10,350 and r = average incremental increase = 320 (from Table 5.3) P, = 74100 + 2 x 10350 + 20+) x 320 = 95760. 4. Graphical Extension Method Fig. 5.2 shows the plot between the population and the time. The dotted portion of the curve is the extended part from 1991 to 2011, following closely its trend. From the extended part, the population at the end of 2011= 80,000. 5. Decreased Rate of Growth Method Column 6 of Table 5.3 gives the decrease in the per cent increment found in column 4. In the initial portion of the census records, there is no decrease in the percent increment, and hence this period has not been included in the computations. The total decrease in percent increment for four decades comes out to be 53.45, giving an average rate of decrease in the percentage growth = 38 AS _ 13. 36% In column 4, the average increment rate per decade was found to be 36.76%, but due to decrease in the rate of growth, this figure will be modified as under :aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.156 WATER SUPPLY ENGINEERING 5.6. WATER DEMAND An average person may consume no more than 5 to 8 litres a day in liquid and solid foods, including 3 to 6 litres in the form of water, milk and other beverages. However, the per capita con- sumption of water drawn from public supply is quite large. Total water requirements may be divided into the following five categories: Residential or domestic use. Institutional use. Public or civic use. Industrial use. Water system losses. Pepe pe per 1. Residential or domestic use The residential or domestic use includes water requirements for drinking, cooking, bathing, washing of clothes, utensils and house, and flushing of water closets. Provision is sometimes made for domestic animals. IS : 1172-1957 recommends a per capita water consumption of 135 litres per day. Table 5.5 gives the break up of water requirements for domestic purposes, which forms about 50% of the total water requirements per head per day, for all the five categories mentioned above. Table 5.6 gives the water requirements for domestic animals. It should be noted that water required for lawn sprinkling and for residential gardens is over and above the values given in Table 5.5. TABLE 5.5. WATER REQUIREMENTS FOR DOMESTIC PURPOSES Bathing Washing of clothes Flushing of W.C. Washing the house Woshing of utensils Cookingaa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.160 WATER SUPPLY ENGINEERING The above formulae for water demand do not take into account the frequency of fire that may occur. It may be determined from the following expression : 436078 ‘ = — 5 litres/minute (5.21 (t+ 120% aly where t = duration of fire in minutes T = period of occurrence of fire, in years. The recommended minimum values for the above formula are: ¢ = 30 minutes and T=1 year The manual on water supply and Treatment by MUD recom- mends that a provision in kilo litres per day based on Eq. 5.22, where P is the population in thousands may be adopted for com- munities larger than 50,000 : Q=100VP vwe(5.22) It is desirable that one third of the fire fighting requirements form the part of service storage. Thus, for a population of 100,000, Q will be = 100 V 100 = 100 kilo litres per day. 4. Industrial use The presence of industries in or near the city has great impact on the water demand. The quantity of water required depends upon the type of industry. For a city with moderate factories, a provision of 20 to 25 percent of per capita consumption may be made for this purpose. The fore cast for this demand will be based on nature and magnitude of cach industry and the potential for its expansion. Table 5.9 gives data about the needs of some industries. TABLE 5.9. INDUSTRIAL NEED. Industry Unit of Water requirement in production kilolitres per unit Automobile Vehicle 40 Distillary Kilolitre (proof alcohol) 122-170 Fertilizer Tonne Leather 100 kg (tonne) Paper Toone Special quality paper | Toone Straw board Tonne Petroleum refinery | Tonne (crude) Steel Tonne . Sugar Tonne (cane crushed) . Textile 100 kg (goods) 1. 2 3. 4 5. 6. 2. 8. oaa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.164 WATER SUPPLY ENGINEERING consumption will be = xrexi. 5=16.9 litres/hour. The absolute maximum hourly demand (adopting the monthly and seasonal factors suggested above) will be = 2 x 1.30 1.40x 1.80% 1.50 = wx 4.914=30.7 litres/hour (against an annual average of = 6.25 litres hour). In order to cope with the hourly variations in the demand, either the pumps may be run at variable speed (which is difficult and cymbersome) or else the pumps may be run at average speed and store the water during the period of less consumption. The second alternative is generally followed. If the pumps are run for all the 24 hours, the rate of delivery by the pumps will be equal to average demand. If they are run only for ¢ hours in a day, the Tate of pumping will be 2 times the average consumption. The excess water during the slack demand period is stored in a service reservoir, to be consumed during the’ periods of peak demand. Effect of Variation in Consumption on Design A water supply system has several units, and design of each unit should match with the hourly, daily and seasonal variations in the demand. The design principles taking into account the effect of variation in the consumption are given below : 1. Filters and pumps. The filter units as well as pumping units are designed for 1.50 times the average daily demand. For example, if the annual average consumption is 150 litres/capita/day, and the population is 50,000, the filter units are designed for 1.50 x 50,000 = 75,000 litres capacity. Similarly, the pumps are desig- ned to deliver 75,000 litres of water in 24 hours. If, however, the pumps are worked only for 12 hours, their hourly discharge will » 75000 12 = 6250 litres per hour. 2. Distribution mains. Distribution mains are designed for the maximum hourly demand of the maximum day. Adopting the factors suggested above, the multiplying factor for the supply will be =18x 15=2.7. 3. Sedimentation tanks and water reservoirs. The sedimentation tanks and the clean water reservoirs are designed for the average daily rate of consumption.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.168 WATER SUPPLY ENGINEERING TABLE 6.1. SUSPENDED AND DISSOLVED IMPURITIES Type Constituents Effect 1 Suspended Impurities 2. Dissolved Impurities (a) Bacteria (6) Algae, Protozoa (c) Silts (@) Sats () Calcium and Magnesium Bicarbonate \_carbonate ‘Sulphate —Chioride Bicarbonate {Carbonate Sulphate Fluoride (i) Sodium hioride (8) Metals and Compounds () Iron oxide Manganese Lead Anscenie Barium Cadmium Cyanide Boron @) Silver Nitrates @i) (©) Vegetable dyes (@) Gases +—-Carbon dioxide \_Hydrogen sulphide Some cause diseases Odour, colour, turbidity Murkiness or turbidity Alkalinity Alkalinity, hardness Hardness Hardness. corrosion Alkalinity, softening effect Alkalinity, softening effect Foaming in boilers Dental flurosis or mottled enamel Taste Taste red colour, corrosive- ness, hardness Black or brown colour Cumulative poisoning Toxicity, poisoning Toxic effect on heart, nerves Toxic, illness Fatal Affect central nervous system, Highly toxic to animals, fish Discolouration of skin; eyes Blue baby conditions; infant poisoning; colour ; acidity Corrosiveness to metals Acidity, corrosiveness Odour, acidity, corro- sivenessaa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.172 WATER SUPPLY ENGINEERING 4. Thermal stratification resulting in low D.O., dissolution of iron and manganese, production of H;S, increase in CO, and reduction in pH. TABLE 6.2 INFLUENCE OF IMPOUNDMENT ON WATER QUALITY Benefits Detriments ‘Turbidity reduction . Less mixing and less reaeration. Hardness reduction . Algal blooms : bad taste and odour Organic oxidation . Back up of pollutants B.O.D. reduction . Thermal stratification Colour reduction (Low dissolved oxygen Coliform reduction (i) Iron and mangenese dissol- ution (ii) Hydrogen sulphide produc- tion (iv) Increase in CO? (*) Reduction in pH. Thermal stratification Thermal stratification is the term which is applied to the variation in the temperature of the impounded water with depth. Fig 6.3 shows thermal stratification in a reservoir, during summer. The entire depth can be divided into three zones: (i) Epilimnion (ii) Mesolimnion (or thermocline) and. (ii) Hypolimnion. WATER SURFACE _ | EPILIMNION 80°F INFLOW FIG. 6.3. SUMMER STRATIFICATION. @ Epilimnion : This is the top zone, 6 to 15 m deep according to depth of reservoir. The water in this zone is of good quality, having high dissolved oxygen.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.176 WATER SUPPLY ENGINEERING 0.1°C, range 0 to 50°. In case of large bodies of surface water, where it is required to record temperature at a certain depth, ‘broken capillary thermometer’ is used. At depths greater than 15 m, a ther- mo-couple may be used. Temperature measurements are sometimes important to identify the magnitude of density, viscosity, vapour pressure and surface tension of water. Other factors such as saturation values of solids and gases dissolved in it, B.O.D. values and the biological activities are dependent on temperature of water. 4, TURBIDITY TEST Turbidity is imparted by the colloidal matter present in water. The colloidal matter may be clay and loam or microscopic organisms. It is a measure of the resistance of water to the passage of light through it. Hence turbidity is estimated against standard suspensions of a siliceous material such as Fuller’s earth, the silica scale being based on standardization by photometric means. The standard unit of turbidity is the turbidity produced by one part of Fuller's earth in a million parts of distilled water. Turbidity is expressed in terms of parts of suspended matter per million parts of water by weight, abbreviated as p.p.m. One unit or 1 p.p.m. is equivalent to 1 mg per litre. The permissible turbidity of domestic water may be between 5 to 10 p.p.m. The following are common methods of measuring turbidity of water : (i) by turbidity rod (i) by Jackson’s turbidimeter (iii) by Baylis turbidimeter (iv) by Nephelometers. (i) Turbidity Rod. Turbidity rod is used for measuring turbidity of water in the field. It consists of a graduated alumininum rod, about 20.3 cm in length, at the upper end of which is attached a graduated non-stretchable tape of about 12.2 cm long. At the lower end of the aluminium rod, a screw containing a platinum needle (of 1 mm diameter and 2.5 cm length) and a nickel ring is inserted. The graduated tape has a mark at its top end specifying the position of eye during the test. In order to find the turbidity, the lower end of the rod is gradually immersed in water whose turbidity is to determined. Eye is kept constantly at the marked position and the platinum needle is watched. The rod is moved slowly in water till the platinum needle just disappears from the vision due to turbidity of water. The reading of the graduated tape near the water surface directly gives turbidity in p.p.m. The rod gives only rough value of the turbidity of water. (ii) Jackson’s Turbidimeter. This is a laboratory apparatus which is used to measure turbidity when it is more than 25 p.p.m., and preferably when it is more than 100 p.p.m. It consists of aaa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.180 WATER SUPPLY ENGINEERING softening. Hardness is expressed either ih p.p.m. or in terms of degrees of hardness. Water is said to have one degree of hardness when its soap destroying power is equivalent to the effect of 14.25 milligrams of calcium carbonate in one litre of water (or 1 gram of calcium carbonate in one imperial gallon). Thus | degree of hardness is equivalent to 1 p.p.m. Table 6.3 gives the nature of water and their scale of hardness in degrees. Table 6.4 gives the hardness in p.p.m. and the corresponding nature of water. TABLE 6.3. Degree of hardness Nature of water Extremely soft water Very soft water Soft water Reasonably soft water Reasonably hard water Hard water Very hard water Excessive hard water Too hard to use. TABLE 6.4. 2 3 4 56-100 101-200 201-500 Slightly Moderately Very hard hard hard There are three methods of determining totai hardness of water (é) Clark’s method, (ii) Hehner’s method. (iii) Versenate method. ( Clark’s method. This method is based on the premise that hardness-producing substances react with soap and form insoluble compounds before latter is produced. Hence total hardness is found by determining the standard soap solution required to obtain a per- manent lather with the water sample of known volume with constant shaking. This method has become obsolete. (ii) Hehner’s method. in this method the temporary hardness is determined by titration with a standard solution of sulphuric acid, using methyl orange as indicator. To determine the permanent hard- ness, standard sodium carbonate solution is added to the water sample and evaporated to dryness. The amount of sodium carbonate inaa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.184 ¥ WATER SUPPLY ENGINEERING {H*] x [OH7] = 10°" at 21°C. In freshly distilled water, concentration of both the ions will be the same. (H*] = 1077 and [OH™] = 107” 5 pH = — logw[H] =—logio{10~"] =7 Also, POH = — logy [OH] = — logy [10-7] =7 Example 6.3. A waste water from a factory having pH = 10 contains KOH only. Find out the total quantity of KOH per day if the waste water discharge is 80m°/day. Soluticn. From Eq. 6.2 (b), we have pH + pOH = 14 pOH =.14 —- pH=14-10=4 [OH] = 107? molesfitre (Note that a ‘mole’ is the molecular weight in g.) Now, molecular weight of KOH is equal to (39+16+1) = 56 g. -. KOH in gflitre = 56 x 10-* Now waste water discharge = 80 m’/day = 80 x 10° litres/day Quantity KOH = (80 x 10°) x (56 x 107°) g/day = 4480 g/day = 4.48 kp/day Example 6.4. Find out the pH of the mixture of the following two solutions : Solution A: volume =500 ml ; pH =7 Solution B : volume = 500 ml ; pH =5 Solution. Since the volume of cach solution is equal, the morality of mixture will be half in 1000_ml. Now, [H*] of 4 =10-’ molefitre and {H*] of B = 107 molefitre [H* Jui = G x 10-7) + x 10-5) = (0.5 x 107’) + (50 x 10°’) = 50.5 x 10~” mole/litre. — logy [H*] [PH]nixaa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.UNIT OPERATIONS 21s (e) Biological floatation @* Vacuum filtration (g) Air drying (A) Heat drying (i) Sludge digestion () Incineration (A) .Wet combustion. The aims of some of these operations one described in sub- sequent articles. 7.3. GAS TRANSFER In this unit operation, the gases are either released/desorbed from water or are dissolved/absorbed in water. This is achieved by exposing the water through spray or bubble aeration to either air or other atmospheres, under normal, increased or reduced pressures. This is an important unit operation which is carried out for water purification to achicve the following. (i) Removal of objectionable gases such as carbon dioxide, hydrogen sulfide and other volatile odorous substances, by spray or bubble aeration. (i) Deferrization and/or demanganisation of water, through the addition of oxygen by spray or bubble aeration. (iii) Addition of ozone from ozone generators or chlorine gas from chlorine dispensers, either for the disinfection of waters or for the destruction of odors and tastes in waters. (iv) Addition of carbon dioxide from the gas or carbon dioxide generators to recarbonate lime softened water. (v) Removal of corrosion-promoting oxygen as well as other gases (degasification) by spraying water into vacuum chamber at or- dinary temperatures or at elevated temperatures. The first two operations of gas transfer, mentioned above, are commonly called aeration. In most instances, the shared engineering objective of aeration is either the removal of gas and other volatile substances from water or their addition to water, or both at the same time. Commonly used aerators fall under four categeries : @_ Gravity aerators (@) Spray aerators (il) Diffusers and (iv) Mechanical aerators.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.UNIT OPERATIONS 219 6. Miscellaneous processes : These include water softening, desalination, removal of iron, manganese and other harmful con- stituents. Fig. 7.1 gives the schematic layout of a water treatment plant. RESERVOIR FIG. 7.1 SCHEMATIC LAYOUT OF WATER TREATMENT PLANT.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.aa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.SCREENING AND AERATION 233 1. Orifice and nozzle behaviour Spray aerators are normally composed of perforated or nozzle pipes which create a spray pattern. The initial spray velocity (v) is given by v=C,V 2gh wi) «.-(810) where C, = velocity coefficient ( ~ 0.95) h = orifice head or driving head. For a pipe having multiple openings, Q =C (Sa) V 2h (ii) ...(8.11) where Q =rate of discharge. C = discharge coefficient =0.8 for rounded openings = 0.85 to 0.92 for nozzles = 0.6 for sharp edged openings Za = total area of openings If there are n openings, each of equal area a, Za =na «»(iii) The water rises either vertically or at an angle (a) and falls onto a collecting apron, after moving along a trajectory. V#O8¥ sina ote TRAJECTORY V sine 80.. Vicos trte tt HO Ftv coset) t ———_ FIG. 89. Let hh =driving head 1, =time of rise of spray t =total time of exposure= 2 ¢, a =inclination of jet. At the time of rise 4, v=0 v=0 =vsina-—geaa You have either reached a page that is unavailable for viewing or reached your viewing limit for this book.