Correl Mock Hydraulics Set A

MOCK BOARD EXAMINATION: HYDRAULICS AND GEOTECHNICAL ENGINEERING MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

INSTRUCTIONS: Read the following problems carefully, answer the questions and choose the answer from the choices provided and shade in the given answer sheet. If your answer is not available in the choices shade letter E. Good luck! SITUATION A: Gate ABC in the figure has a fixed hinge line at B and is 2 m wide into the paper. The gate will open at A to release water if the water depth is high enough.

1) 2) 3)

Compute the force acting on BC if depth h = 1.6 m. A.) 2.35 kN B.) 3.53 kN C.) 12.56 kN D.) 25.11 kN Compute the length “L” for which the gate will begin to open A.) 34.6 cm B.) 35.2 cm C.) 27.8 cm D.) 29.1 cm Compute the depth “h” for which the gate will begin to open if length L = 20 cm and the gate weighs 50 kg acting 5 cm from B. A.) 1.45 m B.) 1.20 m C.) 1.31 m D.) 1.52 m

SITUATION B: The tank in the figure is 3 m wide into the paper. Neglecting atmospheric pressure, compute the following hydrostatic forces on quarter-circle panel BC:

1

MOCK BOARD EXAMINATION: HYDRAULICS AND GEOTECHNICAL ENGINEERING MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

4) 5) 6)

Horizontal force component. A.) 1056.97 kN B.) 1098.72 kN Vertical force component. A.) 1363.79 kN B.) 1255.51kN Resultant force. A.) 1430 kN B.) 1668 kN

C.)

905.97 kN

D.)

941.76 kN

C.)

1076.15 kN

D.)

1481.51 kN

C.)

1406 kN

D.)

1538 kN

SITUATION C: The reading of an automobile fuel gage is proportional to the gage pressure at the bottom of the tank. If the tank is 32 cm deep and is contaminated with 3 cm of water,

7)

8) 9)

If the tank is full of gasoline what should be the reading at the gage in Pa? Use γwater = 9790 N/m^3 and γair = 11.8 N/m^3 A.) 2130 B.) 3132 C.) 1997 D.) 2839 How many centimeters of air remains at the top when the gauge indicates “full”? A.) 1.42 B.) 0.945 C.) 3.75 D.) 4.42 With the contaminated water, what will be the reading in the gauge in Pa if 50 L of gasoline is discharged out? The tank is 0.5 m^2 in area. A.) 1332 B.) 1665 C.) 1760 D.) 1465

SITUATION D: A block of steel (S=7.85) will “float” at a mercury-water interface.

2

MOCK BOARD EXAMINATION: HYDRAULICS AND GEOTECHNICAL ENGINEERING MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

10)

What will be the ratio of the depths a and b for this condition? A.) 0.839 B.) 0.577 C.) 0.623 D.)

0.544

SITUATION E: A 4-in-diameter solid cylinder of height 3.75 in weighing 0.85 lb is immersed in liquid (γ=52 pcf) contained in a tall, upright metal cylinder having a diameter of 5 in. before immersion the liquid was 3.0 in deep. 11) Calculate the depth of submergence of the cylinder. A.) 1.873 in B.) 2.248 in C.) 1.634 in D.) 2.698 in 12) Calculate the rise of liquid surface from the original due to immersion of the cylinder. A.) 1.50 in B.) 1.44 in C.) 1.72 in D.) 1.20 in 13) Calculate the distance of the bottom of the solid cylinder from the bottom of the metal cylinder. A.) 1.80 in B.) 2.33 in C.) 2.47 in D.) 2.19 in SITUATION F: Oil is discharging out of an orifice under a constant pressure of 24 kPa. The vessel is an upright cylinder 4 m in diameter.

14) 15) 16)

3

Calculate the initial head producing the flow. A.) 10.34 m B.) 5.45 m C.) 5.71 m D.) 10.59 m Calculate the instantaneous discharge in L/s. A.) 51.2 B.) 50.0 C.) 68.9 D.) 69.7 Calculate the time to discharge oil from 3 m to 1 m assuming that the pressure of air in the tank remains constant during discharge. A.) 477 s B.) 626 s C.) 859 s D.) 541 s

MOCK BOARD EXAMINATION: HYDRAULICS AND GEOTECHNICAL ENGINEERING MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

SITUATION G: A rectangular channel has b = 3 m and y = 1 m. 17) If n and S are the same, what is the diameter of a semi-circular channel that will have the same discharge? A.) 1.780 m B.) 1.403 m C.) 1.567 m D.) 1.334 m SITUATION H: Water flows in in the series-parallel system of the figure below, all pipes are 8-cmdiameter with Hazen-Williams constant, C = 100. If the total pressure drop p1 - p2 = 750 kPa. Neglect minor losses.

18) 19) 20)

Determine the head loss in the 100-m-long pipe. A.) 16.54 m B.) 20.96 m C.) 12.59 m Determine the head loss in the 150-m-long pipe. A.) 63.86 m B.) 59.91 m C.) 55.49 m Determine the flow rate in the 250-m-long pipe in L/s. A.) 11.56 B.) 9.52 C.) 8.38

D.)

30.03 m

D.)

46.42m

D.)

7.23

SITUATION I: The small turbine in the figure extracts 400 W of power from the water flow. Both pipes have a friction factor of 0.02.

4

MOCK BOARD EXAMINATION: HYDRAULICS AND GEOTECHNICAL ENGINEERING MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

21) 22) 23)

Determine the flow rate in m^3/s. A.) 0.00378 B.) 0.00167 C.) 0.00209 D.) Determine the total head loss in m. A.) 3.15 B.) 2.96 C.) 2.21 D.) Determine the pressure at the suction side of the turbine in kPa. A.) 195 B.) 205 C.) 175 D.)

0.00242 7.22 220

SITUATION J: Oil with a specific gravity of 0.86 discharges from a 250-mm-diameter pipe through a 100-mm-diameter sharp-edged orifice as shown in the figure. Coefficients of velocity and contraction are 0.98 and 0.63, respectively.

24) 25) 26)

Determine the discharge of oil in the pipe in L/s. A.) 39.5 B.) 42.6 C.) 46.6 D.) Determine the diameter of the jet at the vena contracta in mm. A.) 79 B.) 63 C.) 57 D.) Determine the velocity of the jet in m/s. A.) 9.61 B.) 8.49 C.) 8.14 D.)

43.2 84 8.91

SITUATION K: Consider the three-reservoir system shown in the following figure with the following data:

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MOCK BOARD EXAMINATION: HYDRAULICS AND GEOTECHNICAL ENGINEERING MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

L1 = 95 m L2 = 125 m L3 = 160 m z1 = 25 m z2 = 115 m z3 = 85 m All pipes are 28-cm-diameter unfinished concrete (n = 0.013) 27) Compute the steady flow rate in pipe 2 in m^3/s assuming that there is no flow in pipe 3. A.) 0.394 B.) 0.465 C.) 0.271 D.) 0.166 28) Compute the steady flow rate in pipe 3 in m^3/s assuming that there is no flow in pipe 2. A.) 0.549 B.) 0.639 C.) 0.409 D.) 0.521 29) If flow is to occur in pipe 3, compute the steady flow rate in pipe 1 in m^3/s. A.) 0.602 B.) 0.791 C.) 0.437 D.) 0.654 SITUATION L: A clay tile, roughness coefficient of 0.014, V-shaped channel has an included angle of 70° and carries 8.5 m^3/s. Compute the following: 30) The critical depth for uniform flow. A.) 1.97 m B.) 1.33 m C.) 1.72 m D.) 1.25 m 31) The critical velocity in m/s for uniform flow. A.) 3.13 B.) 4.11 C.) 6.86 D.) 7.76 32) The critical slope for uniform flow. A.) 0.00238 B.) 0.00163 C.) 0.00411 D.) 0.00335 33) The minimum specific energy for uniform flow. A.) 2.22 B.) 2.58 C.) 2.46 m D.) 2.83 SITUATION M: A sharp edged weir is to be constructed across a stream in which the normal flow is 200 L/sec. 6

MOCK BOARD EXAMINATION: HYDRAULICS AND GEOTECHNICAL ENGINEERING MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

34) 35)

36)

If the length of the weir is 1.5 m, determine the head on the weir for normal flow. A.) 0.27 m B.) 0.18 m C.) 0.42 m D.) 0.33 m If the maximum flow likely to occur in the stream is 5 times the normal flow then determine the length of weir necessary to limit the rise in water level to 38.4cm above that for normal flow. Cd=0.61. A.) 1.49 m B.) 1.82 m C.) 1.24 m D.) 1.13 m With the calculated length, determine the head on the weir for normal flow. A.) 0.2 m B.) 0.3 m C.) 0.5 m D.) 0.4 m

SITUATION N: A trapezoidal flume of most efficient proportion has a base width of 30. It is laid on a slope of “S”, has roughness coefficient “n”, and discharges 3 cu.m/s when flowing full. 37) 38)

39)

S . n A.) 0.3088 B.) 0.1785 C.) 0.2155 D.) 0.4912 If the flume is to be converted to a most efficient rectangular section, using the same material, what is the resulting depth of the section? A.) 2.25 m B.) 2.75 m C.) 2.50 m D.) 2.00 m How much will the discharge be decreased in cu.m/s? A.) 0.468 B.) 0.732 C.) 0.639 D.) 0.512 Calculate the value of

SITUATION O: You work in the quality control division for an engineering consulting firm. Your company has been hired to design a concrete dam to aid in the creation of a new reservoir. A junior consultant has submitted the final plans for the dam (see figure below). Your job is to check to make sure that the dam is properly designed and will not topple over about its pivot point A (it is assumed that the dam will not slide). In order to do this, you need to figure out at what water depth (h) the dam will topple over. You are given the following data: The depth of the river downstream of the dam is 10 m and is kept constant, the density of the concrete is 2300 kg/m3, the height of the dam is 30 m, the base of the dam is 15 m long, the dam and the reservoir are 100 m wide (into the page), and water cannot leak under the base of the dam.

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MOCK BOARD EXAMINATION: HYDRAULICS AND GEOTECHNICAL ENGINEERING MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

h

30 m

A 40)

41) 42)

10 m

15 m What magnitude of moment in kN·m will the tail water create about the pivot point A? A.) 386,125 B.) 306,563 C.) 204,375 D.) 157,263 At what water depth h will the dam topple over about its pivot point A? A.) 28.90 m B.) 31.85 m C.) 29.75 m D.) 32.60 m At maximum water depth equal to the height of the dam, what is the factor of safety against overturning? A.) 1.376 B.) 1.635 C.) 1.196 D.) 0.987

SITUATION P: A closed cylindrical tank, 1.8 m high and 0.9 m in diameter, contains 1.35 m of water. The air space inside is subjected to a constant pressure of 107 kPa. 43) If the cylinder rotates about its geometric axis at an angular velocity of 12 rad/s, what would be the resulting depth of water at the center of the tank? A.) 1.157 m B.) 0.314 m C.) 0.643 m D.) 0.764 m 44) What is the pressure at the bottom center of the tank? A.) 110.08 kPa B.) 114.50 kPa C.) 111.41 kPa D.) 113.31 kPa 45) What is the pressure at the bottom side of the tank? A.) 121.58 kPa B.) 127.86 kPa C.) 124.65 kPa D.) 118.35 kPa SITUATION Q: A large open tank contains a layer of oil of specific gravity 0.7 floating on water as shown in the figure. Assume the flow is inviscid.

8

MOCK BOARD EXAMINATION: HYDRAULICS AND GEOTECHNICAL ENGINEERING MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

46) 47) 48)

Determine the height, h, which the water will rise in the 0.1 diameter nozzle. A.) 2.8 m B.) 3.5 m C.) 2.5 m D.) 3.8 m Determine the water velocity in the 0.2 m diameter pipe. A.) 3.70 m/s B.) 1.92 m/s C.) 1.85 m/s D.) 3.53 m/s Determine the pressure in the pipe. A.) 37.3 kPa B.) 35.6 kPa C.) 33.5 kPa D.) 31.4 kPa

SITUATION R: A soil in its natural state has moisture content of 36.33% and kN/m3. The specific gravity of soil particles is 2.50. 49) What is the void ratio? A.) 0.69 B.) 0.75 C.) 0.94 50) What is the dry unit weight? A. 11.64 kN/m3 B. 12.63 kN/m3 C. 13.55 kN/m3 51) What is the degree of saturation? A. 96.6% B. 77.6% C. 68.6%

unit weight of 17.22

D.)

1.05

D. 13.69 kN/m3 D. 55.6%

SITUATION S: An embankment has void ratios at loosest and densest state 0.88 and 0.51 respectively. Given that the dry unit weight is 15.6 kN/m3 and G=2.65, determine the following: 52) Void ratio. A. 0.69 B. 0.67 C. 0.56 D. 0.59 53) Relative density. A. 0.577 B. 0.612 C. 0.674 D. 0.685 54) Saturated unit weight in kN/m3. A. 18.77 B. 19.25 C. 21.09 D. 19.52 9

MOCK BOARD EXAMINATION: HYDRAULICS AND GEOTECHNICAL ENGINEERING MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

SITUATION T: A thick clay layer has void ratio 0.68, specific gravity 2.5, capillary constant 0.3 cm2 and effective diameter 12 μm. The ground water table is 10 m below the ground surface. 55) What is the height of capillary rise? A. 4.55 m B. 4.01 m C. 3.68 m D. 3.57 m 56) What is the total pressure 8 m below the ground assuming that the ground above capillary action to be dry? A. 115 kPa B. 123 kPa C.142 kPa D. 138 kPa 57) What is the vertical effective pressure 15 m below the ground that the ground above capillary action to be dry? A. 161 kPa B. 245 kPa C. 204 kPa D. 225 kPa SITUATION U: A sand layer, 6 m thick, is underlain by 5 m thick clay. The clay has a saturated unit weight of 19 kN/m3. The sand has moist and saturated unit weights 16.7 and 18.4 kN/m3 respectively. The ground water table is 3 m below the ground. Point A is 15 m below the ground surface. 58) What is the total pressure at point A? A. 304 kPa B. 289 kPa C. 265 kPa D. 276 kPa 59) What is the pore water pressure at point A? A. 165 kPa B. 118 kPa C. 135 kPa D. 125 kPa 60) What is the effective pressure at point A? A. 158 kPa B. 167 kPa C. 155 kPa D. 123 kPa SITUATION V: The following results were obtained from a liquid limit test on a clay using Casagrande cup device. The natural content of this clay is 36% and plastic limit is 23%. 61) What is the liquid limit? A. 33 B. 39 C. 45 D. 48 62) What is the plasticity index? A. 10 B. 16 C. 18 D. 22 63) What is the nature of the soil? A. plastic B. liquid C. semi-solid D. None in list SITUATION W: Following are the results of a shrinkage limit test: 10

MOCK BOARD EXAMINATION: HYDRAULICS AND GEOTECHNICAL ENGINEERING MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

64) 65) 66)

Initial volume of soil in saturated state = 24.6 cc Final volume of soil in dry state = 15.9 cc Initial mass in saturated state = 44 g Final mass in dry state = 30.1 g What is the shrinkage limit? A. 16.55 % B. 16.79 % C. 17.28 % What is the shrinkage ratio? A. 0.956 B. 1.021 C. 1.452 What is the specific gravity of solids? A. 2.16 B. 2.53 C. 2.81

D. 17.86 % D. 1.893 D. 2.98

SITUATION X: Given the figure is the soil layer of a project site. The proposed building will exert a net stress of 12 Newtons per square cm.

67)

68)

69)

11

Determine the buoyant unit weight of the clay. A. 7.22 kN/m3 C. 8.55 kN/m3 B. 8.28 kN/m3 D. 9.21 kN/m3 Determine the vertical effective stress at the midheight of the clay layer. A. 172.43 kPa C. 179.21 kPa B. 170.65 kPa D. 186.75 kPa Determine the average settlement of the normally consolidated clay layer. A. 165 mm C. 221 mm B. 198 mm D. 233 mm

MOCK BOARD EXAMINATION: HYDRAULICS AND GEOTECHNICAL ENGINEERING MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

SITUATION Y: A soil profile is consisting of a 9-m sand layer over an 8-m clay layer. The ground water table is 3 m below the sand surface. The sand over the ground water table has γdry=16 kN/m3 while below has γsat=18.5 kN/m3. The clay has the following properties: γsat=19 kN/m3, e=0.95 and LL=50%. A uniformly distributed load of 50 kPa is applied at ground surface. Cs=0.2Cc 70) What is the settlement when clay is normally consolidated? A. 150 mm B. 170 mm C. 185 mm D. 200 mm 71) What is the settlement when the preconsolidation pressure is 210? A. 40 mm B. 47 mm C. 53 mm D. 59 mm 72) What is the settlement when the preconsolidation pressure is 145? A. 170.19 mm B. 163.8 mm C. 183.3 mm D. 152.8 mm SITUATION Z: A permeability pumping test was carried out in a confined aquifer with the piezometric level before pumping is 2.18 m below the ground surface. The aquiclude has a thickness of 5.70 m measured from ground surface and the confined aquifer is 7.60 m deep until it reaches the aquiclude at the bottom. At a steady pumping rate of 15.60 m 3/hr, the drawdowns in the observation wells were equal to 1.62 m and 0.47 m, respectively. The distances of the observation wells from the center of the test well are 15 m and 32 m respectively. 73) Compute the depth of water at the farthest observation well. A. 10.65 m B. 12.83 m C. 7.13 m D. 9.31 m 74) Compute the coefficient of permeability in m/s. A. 0.215 B. 5.98x10^-5 C. 0.162 D. 4.51x10^-5 75) Compute the transmissibility. A. 1.634 B. 1.231 C. 0.00034 D. 0.00045 SITUATION AA: The following data were obtained from sand-cone experiment where a volume of a certain soil is replaced with a sand in order to find the density of the soil. Density of sand used in test = 1.3 g/cc Wt. Of soil excavated from the pit = 925 g Wt. of sand filling the pit = 675 g Water content of natural soil = 15% 12

MOCK BOARD EXAMINATION: HYDRAULICS AND GEOTECHNICAL ENGINEERING MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

Specific gravity of Solid = 2.7 76) Determine the wet density of the soil in g/cc. A. 2.01 B. 1.65 C. 1.83 77) Determine the dry density of the soil in g/cc. A. 1.65 B. 1.55 C. 1.49 78) What is the porosity of the soil? A. 0.74 B. 2.89 C. 0.43

D. 1.78 D. 1.33 D. 1.07

SITUATION AB: A soil sample has a dry unit weight of 17.79 kN/m3 and a void ratio of 0.50. 79) What is the specific gravity of soil solids? A. 2.65 B. 2.67 C. 2.72 D. 2.75 80) What is the saturated unit weight of the sample in kN/m3? A. 19.08 B. 20.42 C. 21.06 D. 22.31 81) What is the hydraulic gradient at quicksand condition? A. 1.42 B. 1.15 C. 1.28 S. 1.19 SITUATION AC: A consolidated-undrained test on a normally consolidated clay provided that the cell pressure is 140 kPa, the deviator stress at failure is 125 kPa and the pore water pressure is 75 kPa. 82) What is the normal stress corresponding to maximum shear stress in drained condition? A. 130.5 kPa B. 127.5 kPa C. 133.5 kPa D. 136.5 kPa 83) What is the shear stress at the point of failure plane in drained condition? A. 62.5 kPa B. 63.9 kPa C. 54.5 kPa D. 49.7 kPa 84) What is the drained angle of friction? A. 29.35° B. 17.89° C. 16.87° D. None in list SITUATION AD: The results of two drained tri-axial tests on a saturated clay are given in the table. Test Cell Pressure Deviator Stress A 120 kPa 215 kPa B 200 kPa 350 kPa

13

MOCK BOARD EXAMINATION: HYDRAULICS AND GEOTECHNICAL ENGINEERING MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

85) 86) 87)

What is the cohesion of the soil? A. 7.5 kPa B. 3.8 kPa C. 12.1 kPa What is the angle of friction of the clay? A. 33° B. 21° C. 27° What is the maximum shear of test A? A. 107.5 kPa B. 106 kPa C. 101.2 kPa

D. 10.2 kPa D. 35° D. 195 kPa

SITUATION AE: A consolidated drained tri-axial stress is conducted on a normally consolidated clay. The shear stress at failure plane is 185 kPa and the angle of friction is 21°. 88) What is the deviator stress at failure? A. 205 kPa B. 112 kPa C. 405 kPa D. 396 kPa 89) What is the chamber confining pressure? A. 300 kPa B. 355 kPa C. 321 kPa D. 195 kPa 90) What is the maximum principal stress? A. 553 kPa B. 751 kPa C. 994 kPa D. 1021 kPa SITUATION AF: A consolidated drained tria-axial test was conducted on a cohesionless soil that has a friction angle of 28° and deviator stress at failure of 380. 91) What is the confining pressure in kPa? A. 194.7 kPa B. 201.9 kPa C. 188.7 kPa D. 214.7 kPa 92) What is the angle that the failure plane makes with the major principal plane? A. 60° B. 45° C. 55° D. 59° 93) What is the normal stress at failure plane? A. 315.5 kPa B. 301.2 kPa C. 332.78 kPa D. 320.9 kPa SITUATION AG: A frictionless retaining wall is 7 m high and supports a horizontal backfill with the following properties: dry unit weight = 14.6 kN/m3, saturated unit weight = 19.21 kN/m3, angle of friction = 34°. 94) If the ground water table is very deep, what is the expected total active thrust in the wall if it is 1.5 m wide? A. 101.13 kN B. 151.69 kN C. 133.06 kN D. 199.59 kN

14

MOCK BOARD EXAMINATION: HYDRAULICS AND GEOTECHNICAL ENGINEERING MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

95)

96)

If the ground water table is 3.5 m deep and the soil above the water table is dry, what is the magnitude of the active force in kN per meter of the wall? A. 152.24 B. 92.15 C. 101.66 D. 112.43 If the ground water table is 3.5 m deep and the soil above the water table is dry, what is the distance of the total active force from the top of the wall? A. 4.55 m B. 2.45 m C. 5.06 m D. 1.94 m

SITUATION AH: A 6.5-m long prestressed concrete pile has a cross section in a form of regular hexagon with side length 310 mm. It is penetrated in a clayey soil with angle of friction ø=31°, unit weight γ=16.5 kN/m3, coefficient of friction α=0.8 and unconfined shear strength of 95 kPa. 97) What is the end bearing capacity of the clay in kN? A. 109.5 B. 213.5 C. 226.5 D. 251 98) What is the developed friction in kN? A. 1035 B. 919 C. 879 D. 1022 99) What is the ultimate load that the pile can carry in kN? A. 1144.5 B. 1132.5 C. 1105.5 D. 1273 SITUATION AI: A uniform soil deposit has a dry unit weight of 15.6 kN/m^3 and a saturated unit weight of 17.2 kN/m^3. The ground water table is at a distance of 4 m below the ground surface. Point A is at a depth of 6 m below the ground surface. 100) Calculate the effective stress at A in kPa. A.) 77.18 B.) 96.80 C.) 83.58 D.) 73.98

15