Hydraulics and

Geotechnical
Engineering
Module 3

CE Department – College of Engineering

Compiled
Compiled
by: by:
Engr.
Engr.
Marbel
Marbel
Perez
Perez Engineering Correlation
Bulacan State University
CE Department – College of Engineering Compiled by: Engr. Marbel Perez

Chapter 3 Hydraulics and Geotechnical Engineering

3.1 Mechanics of Fluids

3.2 Hydraulics

3.3 Geotechnical Engineering – Soil Mechanics

3.4 Geotechnical Engineering – Foundation Engineering

Duration: 30 hours

Introduction

This module will serve as a reviewer for the Civil Engineering Licensure Examination. It

contains a compilation of useful formulas for the subjects of Mechanics of Fluids,

Hydraulics, Soil Mechanics and Foundation Engineering. It is worth noting that this

module will only contain a summarized style of presentation as this subject, CE

Correlation, contains all the topic discussed in the whole Civil Engineering course,

therefore the sheer amount of topics if it is not summarized, will make this unnecessarily

long.

Objectives

1. To be able solve problems in the Civil Engineering Licensure Examination in the

subjects of;

2. Mechanics of Fluids,

3. Hydraulics,

4. Soil Mechanics and

5. Foundation Engineering

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Pre-Test

SITUATION 1: Two footings rest in a layer of sand 2.7 m thick. The bottom of the

footings are 0.90 m below the ground surface. Beneath the sand layer is a 1.8 m clay

layer. Beneath the clay layer is a hard pan. The water table is at a depth of 1.8 m below

the ground surface.

Compute the stress increase at the center of the clay layer assume that the pressure

beneath the footing is spread at an angle of 2 vertical to 1 horizontal.

a. 36.55 kPa b. 21.18 c. 25.51 d. 30.18

Determine the size of footing B so that the settlement in the clay layer is the same

beneath footings A and B. Footing A is 1.5 m square.

a. 3.24 m b. 4.18 c. 3.78 d. 4.77

Determine the settlement beneath footing A.

a. 82.11 mm b. 46.65 c. 54.18 d. 56.75

SITUATION 2: A 600 mm pipe connects two reservoir whose difference in water surface

elevation 48 m. The pipe is 3500 m long and has the following pipe fittings: 2 globe

valves, 4 short radius elbows, 2 long radius elbows, and one gate valve half open. The

values of loss factors for pipe fittings are given (see Gillesania’s Fluid Mechanics and

Hydraulics).

Using the equivalent length method, assuming f = 0.015, calculate the actual length of

the pipe.

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a. 4483 m b. 4064 c. 4199 d. 4318

Determine the head loss of the pipe.

a. 55 m b. 51 c. 48 d. 40

Calculate the flow of the entire pipe system.

a. 861 L/s b. 918 c. 648 d. 744

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3.1 Mechanics of Fluids

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3.2 Hydraulics

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3.3 Geotechnical Engineering – Soil Mechanics

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3.4 Geotechnical Engineering – Foundation Engineering

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Post Test

Mechanics of Fluids

SITUATION 1: A hollow cylinder 1.0 m in diameter and 2.8 m long weighs 3.84 kN.

Determine the weight of lead (unit weight = 110 kN/m3)must be fastened to the outside

bottom to make the cylinder float vertically with 2.3 m submerged in fresh water.

a. 18.55 b. 15.25 c. 12.70 d. 17.54

Determine the weight of lead must be placed inside the cylinder to make the cylinder

float vertically with 2.3 m submerged in fresh water.

a. 17.96 b. 12.70 c. 13.88 d. 14.54

Calculate the additional load assuming the lead is placed inside the cylinder to make the

top of the cylinder flushed with the water surface?

a. 3.85 kN b. 5.70 c. 8.36 d. 7.33

SITUATION 2: An open cylindrical tank having a radius of 0.30 m and a height of 1.20

m is filled with water at a depth of 0.90 m.

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How fast will it be rotated about its vertical axis if half of its volume is spilled out?

a. 191.54 rpm b. 178.34 c. 156.21 d. 145.84

Find the speed of rotation about its vertical axis so that no water will be spilled out?

a. 132.85 rpm b. 121.70 c. 133.84 d. 109.21

Determine the speed of rotation about its vertical axis to produce zero pressure with

0.20 m from the center of the tank.

a. 207.22 rpm b. 222.75 c. 198.56 d. 211.45

SITUATION 3: If 12 m^2 of nitrogen at 30° C and 125 kPa absolute pressure is

expanded isothermally to 30 m^3, use k = 1.40 and constant = pV^k for an isentropic

condition.

Find the resulting pressure.

a. 75 kPa b. 50 c. 45 d. 30

Find the pressure in an isentropic condition.

a. 34.7 kPa b. 44.1 c. 50 d. 62.4

Find the temperature in an isentropic condition. Use T2/T1 = (p2/p1)^(k-1)/k

a. -30°C b. 30°C c. -63°C d. 63°C

If K = 2.2 GPa is the bulk modulus of elasticity of water, what pressure is required to

reduce a volume by 0.6 percent?

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a. 15.7 MPa b. 12.5 c. 14.5 d. 13.2

These are the liquids that vaporizes easily.

a. Ideal b. Newtonian c.Volatile d. Bingham

SITUATION 4: In the figure shown below after the question, Find the draft of the

cylinder.

a. 0.655 m b. 0.485 c. 1.031 d. 0.933

Find the center of buoyancy from the bottom of the cylinder.

a. 0.650 b. 0.375 c. 0.466 d. 0.500

Determine the metacenter below the center of buoyancy.

a. 0.154 m b. 0.125 c. 0.241 d. 0.186

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SITUATION 5: The canal shown in cross section in the figure runs 40 m into the paper.

Determine the horizontal hydrostatic force. Use unit weight = 9.79 kN/cu m

a. 65,112 kN b. 63,439 c. 61,127 d. 58,786

Determine the magnitude of the hydrostatic force.

a. 175,002 kN b. 118,130 c. 154,207 d. 131,284

Find the vertical location of the center of pressure from A.

a. 8.33 m b. 9.54 c. 11.55 d. 9.07

SITUATION 6: A rectangular tank if internal width of 5 m as shown in the figure,

contains oil of sp gr = 0.8 and water.

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Find the depth of oil, h.

a. 1.75 m b. 1.55 c. 1.30 d. 1.25

Find the volume displaced by the block if a 1000 N block of wood is floated in the oil.

a. 1.274 m b. 1.057 c. 1.139 d. 1.047

Find the rise in free surface of the water in contact with air?

a. 17.5 mm b. 13.6 c. 15.7 d. 10.6

SITUATION 7: A tank contains oil (s = 0.80), gasoline (s = 0.90) and sea water (s =

1.03). If the depths of the liquids are 0.5 m ,0.8 m and 1 for oil, gasoline, and sea water

respectively.

Determine the pressure at a depth of 1.2 m

a. 19.62 kPa b. 10.10 c. 15.74 d. 18.33

Determine the pressure at the depth of 1.8 m.

a. 17.55 b. 18.07 c. 19.12 d. 16.04

Determine the presuure throughout the bottom.

a. 20.77 b. 29.12 c. 22.19 d. 21.09

SITUATION 8: The buoy in figure shown has 80 N of steel weight attached. The buoy

has lodged against a rock 2 m deep. Assume the weight of water is 45.62 N,Determine

the length L of the submerged buoy.

a. 2.33 m b. 1.75 c. 1.5 d. 2

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Determine the angle with the horizontal at which the buoy will lean assuming the rock

exerts no moment on the buoy.

a. 45° b. 53° c. 55° d. 59°

Hydraulics

SITUATION 1: A diverging tube discharges water from a reservoir at a depth of 10 m

below the water surface. The diameter of the tube gradually increases from 150 mm at

the throat to 225 mm at the outlet as shown in the figure.

Neglecting friction, determine the maximum possible rate of discharge through this tube.

a. 0.775 m^3/s b. 0.618 c. 0.557 d. 0.481

Determine the corresponding pressure at the throat.

a. -618.04 kPa b. -398.75 c. -188.15 d. -97.16

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SITUATION 2: For the pump shown in the figure, the total friction head loss is 6 m. If the

pump delivers 40 kW of power to the water,

Determine the exit velocity of the water.

a. 32.7 m/s b. 51.4 c. 66.8 d. 18.3

Determine the flow rate.

a. 48.1 L/s b. 48.5 c. 69.6 d. 64.2

Benzene flows through a 100 mm pipe at a mean velocity of 3 m/s. Find the volume flow

rate.

a. 1844 L/s b. 1416 c. 1233 d. 1655

SITUATION 3: A 25 mm long smooth brass pipe 300 m long drains an open 1.2 m

cylindrical tank which contains oil having density = 950 kg/m^3 and dynamic viscosity of

0.03 N.s/m^2. The pipe discharges at elevation 30 m. The liquid surface of oil is at

elevation of 36 m.

Find Reynold’s number for oil.

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a. 88.4 b. 96.1 c. 112.7 d. 144.8

Determine the velocity of flow.

a. 0.1174 m/s b. 0.1488 c. 0.1213 d. 0.1459

Determine the time required in hours for the oil level to drop from elevation 36 to

elevation 32.5 m.

a. 29.6 hours b. 20.4 c. 22.9 d. 27.7

These are the causes of minor losses EXCEPT:

a. Sudden contraction b. Bends c. Valves d. Changes in water flow

An orifice has a coefficient of discharge of 0.62 and a coefficient of contraction of 0.63.

Find the coefficient of velocity for the discharge.

a. 0.884 b. 0.984 c. 0.655 d. 0.800

This formula in pipes is most commonly used in waterworks.

a. Darcy-Weisbach b. Manning c.Hazen-Williams d. Chezy

This refers to the overflowing stream in a weir.

a. Suppressed b. Nappe c. Head d. Contracted

SITUATION 4: The head loss in 74 m of 150 mm diameter pipe is known to be 9 m

when oil (s = 0.90) flows at 0.057 m^3/s. Assume viscosity of oil is 0.0389 Pa.s

Determine the Reynolds number.

a. 11210 b. 13170 c. 15140 d. 19830

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Determine the friction factor “f”.

a. 0.019 b. 0.034 c. 0.044 d. 0.078

Find the shear stress at the wall of pipe.

a. 39.91 N/m^2 b. 48.19 c. 56.23 d. 60.18

SITUATION 5: A 600 mm pipe connects two reservoir whose difference in water surface

elevation 48 m. The pipe is 3500 m long and has the following pipe fittings: 2 globe

valves, 4 short radius elbows, 2 long radius elbows, and one gate valve half open. The

values of loss factors for pipe fittings are given (see Gillesania’s Fluid Mechanics and

Hydraulics).

Using the equivalent length method, assuming f = 0.015, calculate the actual length of

the pipe.

a. 4483 m b. 4064 c. 4199 d. 4318

Determine the head loss of the pipe.

a. 55 m b. 51 c. 48 d. 40

Calculate the flow of the entire pipe system.

a. 861 L/s b. 918 c. 648 d. 744

SITUATION 6: A rectangular irrigation canal 6 m wide contains water 1 m deep. It has a

hydraulic slope of 0.001 and a roughness coefficient of 0.013.

Evaluate the mean velocity of the water in the canal in m/s.

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a. 6.11 m/s b. 2.01 c. 4.66 d. 1.99

Evaluate the discharge in the canal m^3/s.

a. 15.55 m^3/s b. 18.34 c. 14.15 d. 12.06

What would be the depth of the canal in meters using the more economical proportions

but adhering to the same discharge and slope.

a. 1.89 m b. 1.55 c. 1.67 d. 1.38

Water from a reservoir through a non-rigid 600 mm pipe with a velocity of 2.5 m/s is

completely stopped by a closure of a valve situated 200 m from the reservoir. Assume

that the pressure increases at a uniform rate and that there is no damping of the

pressure wave. The pipe has a thickness of 20 mm, bulk modulus of water is 2.2 x 10^9

Pa and modulus of elasticity of steel is 1.4 x 10^11 Pa. Compute the celerity of pressure

wave.

a. 1885 m/s b. 1544 c. 1618 d. 1223

Soil Mechanics

SITUATION 1: A uniform soil deposit has a dry unit weight of 15.6 kN/m3 and a

saturated unit weight of 17.2 kN/m3. The ground water table is at a distance of 4 m

below the ground surface. Point A is at depth of 6 m below the ground surface.

Compute the effective stress at A.

a. 51.02 kPa b. 48.45 kPa c. 54.27 d. 42.39

If the water table goes up by 3.5 m find the effective stress at A.

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a. 44.34 kPa b. 41.02 c. 47.46 d. 48.12

In comparison to 1 and 2, what will happen to the effective stresses at A if the ground

water surface will rise up the ground surface?

a. Increase b. Remain c. Decrease d. Cannot be determined

SITUATION 2: A soil sample was determined in the laboratory to have a liquid limit of

41% and a plastic limit of 21.1%. If the water content is 30%,

Determine the plasticity index.

a. 21.1 b. 19.9 c. 9.9 d. 11.1

Determine the liquidity index.

a. 0.507 b. 0.608 c. 0.394 d. 0.447

What is the characteristic of soil?

a. Brittle b. Liquid c. Dense d. Plastic

SITUATION 3: A consolidated drained tri-axial test was conducted on a normally

consolidated clay. The results as follows:

Chamber confining pressure: 138 kPa Deviator Stress = 258 kPa Compute the friction

angle of the soil.

a. 32.55° b. 21.07° c. 28.89° d. 35.15°

Compute the normal stress at failure.

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a. 204.68 kPa b. 212.59 c. 278.87 d. 255.15

Compute the shear stress at failure.

a. 137.15 kPa b. 112.95 c. 108.53 d. 111.31

SITUATION 4: Refer to the figure. Given q1 = 300 kN/m, q2 = 260 kN/m, x1 = 4 m, x2 =

3 m and z = 3 m.

Find the vertical stress increase at point A due to first line load.

a. 1.75 kPa b. 1.61 c. 1.53 d. 1.44

Find the vertical stress increase at point A due to the second line load.

a. 13.79 kPa b. 14.44 c. 16.78 d. 12.31

Find the total vertical stress at point A.

a. 15.54 kPa b. 18.39 c. 15.32 d. 13.75

SITUATION 5: A certain soil deposit has a liquid limit of 47% and a plastic limit of 24%.

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Compute the coefficient of earth pressure at rest of this soil deposit. Hint: Ko = 0.19 +

0.223log(PI)

a. 0.507 b. 0.447 c. 0.239 d. 0.319

Compute the total stress at rest lateral earth pressure a depth of 5 m. in a dense sand

deposit where this soil was obtained. Unit weight of sand is 18.4 kN/m3.

a. 45.33 kPa b. 46.64 c. 48.33 d. 50.01

Compute the total stress at rest lateral earth pressure at a depth of 5 m in the same

sand deposit but a water table is located at a ground surface. Saturated unit weight of

sand is 20.5 kN/m3.

a. 84.31 kPa b. 80.64 c. 76.15 d. 72.21

SITUATION 6: Specifications on a job required a fill using borrowed soil to be

compacted at 95% of its standard Proctor maximum dry density. Tests indicate that the

maximum is 19.5 kN/m3 with 12% moisture. The borrow material has a void ratio of

0.60 and a solid specific gravity of 2.65.

Compute the dry unit weight of the compacted soil.

a. 17.216 kN/m3 b. 18.525 c. 15.132 d. 19.761

Compute the wet unit weight of the compacted soil.

a. 21.2 kN/m3 b. 20.7 c. 19.6 d. 18.5

Find the required minimum volume of borrow soil required to fill one cubic meter.
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a. 1.38 m3 b. 1.65 c. 1.14 d. 1.29

SITUATION 7: A confined aquifer underlies an unconfined aquifer as shown in the

figure.

Compute the equivalent horizontal coefficient of permeability.

a. 34.17 m/day b. 36.25 c. 38.19 d. 40.01

Compute the hydraulic gradient.

a. 0.0075 b. 0.0080 c. 0.0100 d. 0.0075

Compute the flow rate in cu m per day per meter.

a. 13.76 b. 11.65 c. 10.83 d. 12.91

Foundation Engineering

SITUATION 1: Two footings rest in a layer of sand 2.7 m thick. The bottom of the

footings are 0.90 m below the ground surface. Beneath the sand layer is a 1.8 m clay

layer. Beneath the clay layer is a hard pan. The water table is at a depth of 1.8 m below

the ground surface.

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Compute the stress increase at the center of the clay layer assume that the pressure

beneath the footing is spread at an angle of 2 vertical to 1 horizontal.

a. 36.55 kPa b. 21.18 c. 25.51 d. 30.18

Determine the size of footing B so that the settlement in the clay layer is the same

beneath footings A and B. Footing A is 1.5 m square.

a. 3.24 m b. 4.18 c. 3.78 d. 4.77

Determine the settlement beneath footing A.

a. 82.11 mm b. 46.65 c. 54.18 d. 56.75

SITUATION 2: A concrete pile having a diameter of 0.30 m is to be driven into a loose

sand having a unit weight of 20 kN/ cu m. The pile has a length of 12 m. Coefficient of

friction between the sand and pile is 0.4. Bearing capacity factor Nq = 80. The shaft

lateral pressure factor K is equal to 0.90. Allowable load of the pile is 170 kN.

Compute the ultimate bearing capacity of the pile.

a. 345.9 kN b. 339.3 c. 321.2 d. 315.6

Compute the ultimate frictional capacity.

a. 211.7 b. 213.8 c. 216.8 d. 220.

Find the factor of safety.

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a. 4.79 b. 4.02 c. 3.25 d. 3.11

SITUATION 3: A 7 m deep braced cut in sand is shown in the figure. In the plan the

struts are placed at a spacing of 2 m center to center. Using Peck’s empirical pressure

diagram,

Compute the strut load at level A.

a. 116.18 kN b. 154.77 c. 109.22 d. 128.77

Compute the strut load at level B.

a. 477.54 kN b. 382.53 c. 356.74 d. 339.78

Compute the strut load at level C.

a. 247.83 kN b. 194.16 c. 221.89 d. 203.15

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SITUATION 4: A retaining wall 7 m high is supporting a horizontal backfill having a dry

unit weight of 1570 kg/m3. The cohesionless soil has an angle of fricrion of 34° and a

void ration of 0.68.

Compute the Rankine active force on the wall.

a. 113.87 kN b. 110.65 c. 106.77 d. 101.53

Compute the Rankine active force on the wall if water logging occurs at a depth of 3 m

from the ground surface.

a. 172 kN b. 166 c. 184 d. 153

Compute the location of the resultant active force from the bottom.

a. 1.88 m b. 1.95 c. 2.02 d. 2.18

SITUATION 5: A cantilever sheet pile is 8.2 m long with a depth of embedment of 3.2 m.

Angle of friction of the soil supported by the sheet pile is 34° and has a unit weight of

1.91 g/cc. There is water table below the base of the sheet pile. Use γwater = 9.81

kN/m3.

Compute the active force acting on the sheet pile.

a. 181.2 kN/m b. 155.8 c. 178.3 d. 164.7

Compute the passive force acting on the sheet pile.

a. 373.6 kN/m b. 338.7 c. 326.9 d. 350.8

Compute the theoretical passive force that must be mobilized to ensure stability.

a. 477.9 kN/m b. 505.8 c. 488.3 d. 456.9

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SITUATION 6: In the soil profile shown, the clay layer is normally consolidated and the

ground water location maybe assumed to remain constant. The raft foundation is 15 m x

15 m with a uniform loading of 192 kPa.

Compute the initial effective stress at the midpoint location of clay layer.

a. 142.47 kPa b. 161.85 c. 196.03 d. 207.10

Find the change in stress at mid point of clay?

a. 88.15 kPa b. 90.16 c. 92.17 d. 98.30

Find the settlement due to placement of the raft foundation.

a. 186 mm b. 199 c. 202 d. 209

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It is the direct result of the decrease in the soil volume.

a. Consolidation b. Settlement c. Compressibility d. Transmissibility

He proposed a method based on pressuremeter tests from which the load-settlement

diagrams of foundations can be derived.

a. Meyerhof b. Boussinesq c. Briaud d. Westergaard

SUGGESTED READINGS AND WEBSITES

Das, B. M., & Sobhan, K. (2014). Principles of geotechnical engineering. Stamford:

Cengage Learning.

Knappett, J., & Craig, R. F. (2020). Craig's soil mechanics. Boca Raton, FL: CRC Press,

Taylor & Francis Group.

Potter, M. C., & Wiggert, D. C. (2008). Schaum's outline of fluid mechanics. Dubuque,

IA: McGraw-Hill Contemporary Learning.

Streeter, V. L., & Wylie, E. B. (1985). Fluid mechanics. New York: McGraw Hill.

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References

Das, B. M., & Sobhan, K. (2014). Principles of geotechnical engineering. Stamford:

Cengage Learning.

Knappett, J., & Craig, R. F. (2020). Craig's soil mechanics. Boca Raton, FL: CRC Press,

Taylor & Francis Group.

Potter, M. C., & Wiggert, D. C. (2008). Schaum's outline of fluid mechanics. Dubuque,

IA: McGraw-Hill Contemporary Learning.

Streeter, V. L., & Wylie, E. B. (1985). Fluid mechanics. New York: McGraw Hill.

Various Engineers. (2019). Civil Engineering Board Exam Review Group. Retrieved

2020, from https://www.facebook.com/CEBoardExamPH/.

Answer Key (Post Test)

Answer will be provided later, the post test part of this module will serve as your Plate

no. 3, to be submitted to an agreed upon date. The plate shall contain the full solution

to the problems given in the Post Test. For more information kindly contact Engr Marbel

Perez.

Email: marbel.perez@bulsu.edu.ph

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