Oe REO CIVIL ENGINEERING Preboard Exam 2 Hydraulics and Geotechnical Engineering INSTRUCTION: Select the correct answer for each of the following questions. Mark only one answer for each item by shading the box corresponding to the letter of your choice on the answer sheet provided, STRICTLY NO ERASURES ALLOWED. Use pencil no. 2 only. Situation 1: (1-3) A closed cylindrical vessel, 2 m in diameter and 4 m high is filled with water to a height of 3 m. The rest is filled with air, the pressure of which is 100 kPa. If the vessel is rotated at 152 rpm, determine the following: 1. The distance of the vortex of the water surface below the bottom of the tank. a 127m © b 134m qd. 137m 124m 2. ‘The maximum inside pressure at the base. a -24158kKPa 214.58 KPa b. -23558kKPa sd, 253.58 kPa 3. The minimum inside pressure at the base. a 100KPa & — -12.16kPa b= -8784kPa dP Situation 2: (4-6) A container holds two layers of different liquids, one fluid having a specific gravity of 1.2 is 200 mm deep and the other fluid having a specific gravity of 1.5 is 250 mm deep. A solid spherical metal having a diameter of 225 mm and a sg of 7.4 is submerged such ‘a manner that half of the sphere ison the top layer and. the other half in the bottom layer of fluids, 4, Compute the weight of the spherical metal a 075Ib © 0431b be 275Ib d 243 1b 9. Which of the following most nearly gives the power generated by the turbine in kW? a 18050 © b 23518 a. 215.65 194.27 Situation 4: (10-12) ‘The weight of a certain crown in air is 14 N and its ‘weight in water is 12.7 N. Assuming that the crown is analloy of gold (sp gr = 19.3) and silver (sp gr = 105). Assume unit weight of water = 9.79 kN/m?3. 10. Compute the volume of crown in cubic meters. a 0.008132, c_~——(0,0001328 b—0.0002813d—SS(0.0003281 11. Compute the specific gravity of the crown, a 1067 © 10.77 b& 10.62 ad 10.72 12. Compute the fraction of silver in the crown. a 0535, 0353 b 0.969 d 0.696 ‘Situation 5: (13-15) If the center of gravity ofa ship in the upright position is 10 mabove the center of gravity of the portion under ‘water, the displacement being 1000 metric tons, and the ship is tipped 30 degrees causing the center of ‘buoyancy to shift sidewise by 8m, (Hint: 1 metric ton = 1000 keg) 13. Find the location of the metacenter (in the tilted position) from the bottom of the ship if ts draft is 3m. a 157m © 142m b 124m 4d 175m 14, _ Find the metacentric height.~~. «nw oo Compute the weight of the spherical metal. a 075Ib c 0431b be 2751b ad 2431b 5. Compute the buoyant force acting on the object. a 503N «| 79N be OO7N dd 305N 6 Compute the tension in the wire holding the sphere to ‘maintain its position. a S43N © 534N b354N ad 453N Situation 3: (7-9) Reservoirs A and B have elevations 250 mand 100 m, respectively, and are connected by a pipe having a diameter of 250 mm and a length of 250 m. A turbine is installed at a point in between reservoirs A and B. ‘The discharge in the pipeline is 140 L/s. Use = 120. Which of the following most nearly gives the head loss in the pipe due to friction? a 855m © 917m be 735m ad 615m Which of the following most nearly gives the head extracted by the turbine? a :160.75m 136.10 m b14955m dS 141.45 m 14, 15. ee ees a «157m «142m b 124m d 175m Find the metacentric height. a Sm ce 4m bo 3m a 6m What is the value of the moment in kg-m? a 5000000 «© 6000000 b 3000000 d. 4000000 Situation 6: (13-15) 16. 17. 18. rectangular footing is designed to carry an allowable Toad of 580 kN with its weight inclusive. The bottom of the footing is 1 m below the ground surface and the water table coincides with the bottom of the footing. Assume a general shear failure. Given Y = 18 kN/m*3, C= 25 kPa, Ysat = 21.5 kN/m*3, and = 30 degrees. Ne = 35,Nq = 22, Ny = 19. Determine the width B using FS = 3.0, ifB/L= 0.5 a 0.98 © 077 b 178 a 105 Determine the length L. a 20 «196 bo 154 da 356 Determine width B if the footing is replaced with a square footing. a 1.03 © 1205 b «116 a 178CRF REO CIVIL ENGINEERING Preboard Exam 2 Hydraulics and Geotechnical Engineering 19, It states the relationship between discharge velocity through saturated soils and hydraulic conductivity. a Bernoulli Equation b. Darcy's Law Hazen Equation d. Karman’s Law 20, ‘The moisture content at which the maximum dry unit weight of soil is attained is __ moisture content a optimum © average bs minimum) smaximum, Situation 7: (21-23) ‘An infinite slope has a shear strength parameter at interface of soil and rock as follows: c = 18 kPa, = 25°, p = 1900 kg/m*3. 21, If H=8mand f =20 degrees, find the factor of safety against sliding on the rock surface. a «1472 © 1395 b 1524 a 1657 22, If B=30 degrees, find the critical height in meters. a «116 © 916 bo 877 a 1004 23, If Her = 6 m, find the minimum angle B so that the slope is stable. a 326 © 332 b 353 a 375 Situation 8: (24-26) ‘The consolidation settlement of a new structure founded on a 5 m thick layer is estimated as 6.5 cm. ‘The structure settled by 1.6 cm in 6 months after the completion of construction. If the clay layer is underlain by rock and overlain by a layer of coarse sand, 28 If ground water table was found to be 0.5 m below the footing (Ysat = 21 kN/m3), how much would be the decrease in the ultimate bearing capacity of the foundation in kPa. a 259 © 801 be 1634 a 26 29, Find the allowable bearing capacity using FS = 25, if the ground water table is located 1.5 m above the bottom of the foundation (Ysat = 21 kN/m*3) a 754 © 836 b. 968 a 1052 Situation 10: (30-34) Acutis to be made in a soil havinga unit weight of 18.5, kN/m*3, c= 50 kPa and © = 20 degrees. The side of, the cut slope will make an angle of 45 degrees with the horizontal. 30. If 1=7 mand 0= 15 degrees, find the force that tend to cause sliding in kN. a 3205 © 1196.1 b 3318 ad 12383 31. Find the factor of safety. a 754 ce 558 b 2.76 a 4.76 32, For factor of safety of 3.0, find the value of the critical angle along which the maximum developed cohesion occurs. a 14.76 © 2595 b 19.64 a 34.33 33. Determine the depth of cut (m) for a FS = 3.0. a 1465, 6 12.17 bb 7 a 1188Situation 8: (24-26) ‘The consolidation settlement of a new structure founded on a 5 m thick layer is estimated as 6.5 cm. ‘The structure settled by 1.6 cm in 6 months after the completion of construction. If the clay layer is underlain by rock and overlain by a layer of coarse sand. 24, Determine the degree of consolidation in the first six months. a 028 © 027 b 025 a 026 25, Determine the time required for 50% consolidation to ‘occur in days. a 739 «786 be 825 a 695 26. Determine the amount of settlement which will take place in the next six months in mm. a 25 c 2% bB 23 a 24 Situation 9: (27-29) ‘Asquare footing 1 mx 1 min dimension hasiits bottom located 4 m below the ground surface. The unit weight of soil is 18 kN/m*3 and has a cohesion of 20 kPa. Angle of internal friction is 30 degrees. Nc = 37; Nq = 22;Ny=19. 27. Determine the ultimate bearing capacity (kPa) assuming general shear failure in soil and no presence of ground water table is known. a 2683 2398 Bb 1856 a 1023 ‘occurs. a 14.76 «2595 b 19.64 a 34.33 33, Determine the depth of cut (m) for a FS = 3.0. a 1465 © 1217 bo 7 a 11.88 34. Compute the developed shear stress along the failure plane in kPa. a 459 e434 bo 324 a 222 Situation 11: (35-39) ‘A sand sample is tested in consolidated drained test, with the chamber pressure = 150 kPa, and the deviator stress at failure = 200 kPa 35, Determine the angle of internal friction in degrees. a 2358 © 16.88 b 45 d 14.66 36. Determine the normal stress at failure in kPa a 6.99 «799 b. 209.997 da 11288 37. Determine the shear tress at failure in kPa, a 78.99 c 8899 vb 91.85 a 66.107 38, Determine the maximum shear stress in kPa, a 90 © 7799 b. 100 a 85REO CIVIL ENGINEERING Hydraulics and Geotechnical Engineering 39, Determine the angle of failure plane with respect to 47, _In reference to the previous number, determine the major principal plane. velocity of water in m/s, a 1266 «4599 a 0.645m/s 0.898 m/s be -56.79 ad 30.66 b.— 0.903m/s 0.603 m/s Situation 12: (40-42) Situation 15: (48-49) ‘An embankment with the total volume of 25,000 cu.m. A liquid is discharged from a container through a is tobe constructed asa part of a highway project. The circular orifice having a diameter of 10 mm that is soil to be used in the embankment will come from the located h meters from the liquid surface to the center borrow pit where the average moist unit weight and of the orifice. water content of the soil is 18 kN/m*3 and 10% respectively. Assuming that the soil will be compacted 48, _If the container is open to the atmosphere, obtain the to a dry unit weight of 20 kN/m*3 at a moisture theoretical discharge through the orifice in the content of 15%, liters/sec when h = 9. a 2.13 liters/sec & ——.O4liters/sec 40. Determine the weight of dry soil required in KN. b. 3.09 liters/sec d. 4.01 liters/sec a 500000 © 450000 b. — 435000 ad 409000 49. In reference to the previous number, repeat the question if the container is moving upward at the 41. Determine the volume of borrow required in cu.m. acceleration half that of gravity. a 30550 © 31940 a —-128liters/sec c. ——1.34liters/sec b 27500 a 28720 bd. —-2.38liters/sec d. 1.44 liters/sec 42. Determine the total quantity of water in cum. that 50. An open cylindrical vessel 1.2 m in diameter and 2.1 ‘must be added to the fill during compaction to bring high is 2/3 full of water. Determine the amount of about a desired moisture content of 15%. water in liters that will be spilled out if the vessel is a 2085 © 2548 rotated about the vertical axis at a constant angular b 2217 a 2294 speed of 87 rpm. a 6Oliters « — 70liters © — B0liters ad 90litersbe 2217 ad 2294 Situation 13: (43-45) For a constant permeability on a fine sand, the following data are given: Length of specimen = 15 em Diameter of specimen = 10 cm Constant Head Difference = 40 cm Volume of water collected in 5 mins = S00cc Void ratio of the soil specimen = 0.5, 43, Determine the coefficient of permeability in cm/min. a -1445x10%-3 = 3.556x10°-3 b 7958x103 d,8.998x104-3 44, Dotermine the discharge velocity in cm/min, a 0.021 © 0677 b 0567 0777 45. Determine the seepage velocity in cm/min, a 0899 © 0123 b 0.064 4d 0.899 Situation 14: (46-47) An irrigation canal with trapezoid cross-section has the following dimensions: Bottom width = 2.50 m, depth of water = 0.90 m, side slope = 1.5 horizontal to 1 vertical, slope of the canal bed = 0.001, coefficient of roughness = 0.025. The canal will serve clay-loan Riceland for which the duty of water per hectare is 3.0 liters/sec. 46, Using Manning's Formula, determine the hydraulic radius of the canal, in meter(s) a 0503m & 0.408m Bb. 0.603 m 4 0708m speed of 87 rpm. a « 60 liters 80 liters c a 70 liters 90 liters