BOARD EXAM PROBLEMS:
Hydraulics & Geotechnical Engineering :
Situation 1 :
A prestressed concrete pile, 360mm x 360mm in cross section, is to be driven in a clayey soil
( 𝛾 = 18.5 kN/m3) as shown in the figure. The pile has a design capacity of 360 kN. Use factor
of safety of 2. The unconfined compression shear strength, qu of the soil is 110 kPa. Use Nc
= 9.
Qdesign = 360 kN
L
1. What is the end bearing capacity of pile in kN?
A. 68.43
C. 73.21
B. 64.15
D. 57.93
2. Compute the skin friction in kN expected to develop along the shaft of the pile.
A. 655.8
C. 623.8
B. 783.2
D. 578.5
3. Compute the length of the pile if frictional constant 𝛼 = 0.75?
A. 12.67
C. 11.04
B. 10.58
D. 11.04
Situation 2 :
A confined aquifer is shown in the figure. This aquifer has a source of recharge located as
shown. The hydraulic conductivity of the aquifer is 45m/day with a porosity of 25%. The
piezometer (head) surface in the two observation wells 1650m apart are at elevation 65m
and 60m, respectively from the common datum. The aquifer has an average thickness of 25
m and an average width of 4km.
L
El. 65 m
Aquifer
25 m
4. Determine the nearest value to the rate of flow of water through the aquifer, in cubic
meters per day?
A. 10,606
C. 7,576
B. 16,667
D. 13,636
5. Determine the nearest value to the seepage velocity in m/day?
A. 0.303
C. 0.545
B. 0.424
D. 0.667
6. Determine the nearest value to the time of travel from the head of aquifer to a point 4.2
km downstream in days?
A. 6,300
C. 7,700
B. 13,860
D. 9,900
Situation 3 :
7. A rectangular canal is 5.6meters wide and 1.2 meters depth. The canal is laid on a
uniform slope of 0.002 and roughness coefficient is 0.013?
A. 23.45
C. 18.56
B. 20.58
D. 15.89
8. What savings in lining per meter length of canal could have been affected if the most
efficient ractangular section were used for the same discharge and slope?
A. 0.826 m2 per meter
C. 0.751 m2 per meter
2
B. 0.921 m per meter
D. 0.628 m2 per meter
9. What savings in earth excavation per meter length of canal could have been affected if
the most efficient rectangular section were used for the same discharge and slope?
A. 0.287 m2 per meter
C. 0.171 m2 per meter
2
B. 0.321 m per meter
D. 0.522 m2 per meter
Situation 4 :
A pump draws 24 liters per second of water from reservoir C and lifts it to reservoir D. The
head lost from C to 1 is 3 times the velocity head in the 150-mm suction line and the head
lost from 2 to D is 25 times the velocity head in the 100-mm discharge line.
El. 240 m
C
El. 0 m
D
100 mm
1
150 mm
2
El -20 m
Pump
10. What is the power delivered by the pump to the system in hp?.
A. 73.21
C. 83.87
B. 65.93
D. 79.62
11. What is the pressure head at point 1 in meters of water?
A. 19.62
C. 32.67
B. 23.56
D. 16.58
12. What is the pressure head at point 2 in meters of water?
A. 234.89
C. 271.42
B. 321.67
D. 178.43
Situation 5 :
The result of tri-axial test on a cohesive soil is as follows:
Angle of shearing resistance = 29 °
Cohesion = 31 kPa
Maximum shearing stress = 65kPa
13. Compute for the value of the cell pressure at failure in kPa
A. 15.15
C. 12.15
B. 13.15
D. 14.15
14. Compute for the value of the maximum principal stress at failure, in kPa?
A. 165.15
C. 132.15
B. 154.15
D. 143.15
15. Compute for the value of the normal stress at the plane of maximum shear, in kPa?
A. 78.15
C. 132.15
B. 89.15
D. 143.15
Situation 6 :
A closed conical tank has a bottom radius of 33 cm and is 50 cm tall. The tank contains 0.026
m3 of water?
16. What is the depth of water in the tank in centimetres?
A. 9.65
C. 9.18
B. 8.56
D. 12.34
17. What is the total volume of the tank in cubic meter?
A. 0.094
C. 0.063
B. 0.075
D. 0.057
18. How much water is required to fill the tank in cubic meters?
A. 0.031
C. 0.049
B. 0.068
D. 0.037
Situation 7:
19. Water is flowing in a 200-mm diameter rigid pipe that is 850 m long. The increase in
pressure caused by instantaneous closure of the valve near the exit is 700 kPa. Bulk Modulus
of elasticity of water is 2.07 x 106 Pa.
A. 1528
C. 1321
B. 1439
D. 1639
20. What is the maximum discharge in m3/s?
A. 0.031
C. 0.049
B. 0.068
D. 0.037
21. What is the hammer pressure is expected if the valve is closed in 3 seconds?
A. 365 kPa
C. 567 kPa
B. 1439 kPa
D. 276 kPa
Situation 8 :
A tank 12 m high is to be filled with oil with a unit weight of 9.4 kN/m 3 as shown in the
figure. Neglect the weight of the tank.
GWT
3m
Sand; 𝛾 = 18.88 𝑘𝑁/𝑚3
14
m
e = 1.27
LI = 0.645
PL= 20%
MC = 40%
22. Calculate the compression index of the clay layer.
A. 0.421
C. 0.369
B. 0.346
D. 0.325
23. Calculate the settlement under the center of the tank in mm.
A. 872
C. 723
B. 456
D. 687
24. Calculate the maximum depth to which the tank’s base must be placed to minimize the
settlement?
A. 5.12 m
C. 6.24 m
B. 4.38 m
D. 8.43 m
Situation 9 :
Given the following properties of a soil:
Specific Gravity of solids = 2.70
Void ratio = 73%
Degree of Saturation = 92%
25. Determine the nearest value to the moisture content of the soil.
A. 27.04%
C. 26.45%
B. 28.45%
D. 24.87%
26. Determine the nearest value to the dry unit weight of the soil?
A. 16.43 kN/m3
C. 14.65 kN/m3
B. 17.11 kN/m3
D. 15.31 kN/m3
27. Determine the nearest value to the moisture content when the soil is saturated.
A. 24.87%
C. 26.45%
B. 27.04%
D. 28.45%
Situation 10 :
A thick layer of saturated clay has moisture content of 59%. The specific gravity of soil solids
is 2.68. The water table is on the ground surface.
28. What is the density of clay in grams per cc?.
a. 1.65
C. 1.57
b. 1.78
D. 1.89
29. What is the effective stress at a depth of 30 m?
a. 167.83kPa
C. 476.54 kPa
b. 191.55 kPa
D. 485.85 kPa
30. What is the total stress at a depth of 30 m?
a. 476.54 kPa
C. 485.85kPa
b. 167.83kPa
D. 191.55 kPa
Situation 11 :
A certain liquid flows in a 10-mm-diameter smooth pipe that is 20 m long. The total head
lost in the pipe is 30 m and the Reynolds number is 1800.
31. What is the friction factor f?
a. 0.0238
C. 0.0356
b. 0.0321
D. 0.0287
32. What is the value of the kinematic viscosity of the liquid in m2/s?
a. 1.132 x 10-5
C. 1.921 x 10-5
-5
b. 1.876 x 10
D. 1.598 x 10-5
33. What is the discharge in liters per minute?
a. 15.76
C. 12.21
b. 17.54
D. 13.56
Situation 12 :
The result of tri-axial test on a cohesive soil is as follows:
Maximum axial stress 𝜎1 = 220 kPa
Deviator Stress, 𝜎𝐷 =140 kPa
Angle of shearing resistance, 𝜃=21 °
Cohesion = 31 kPa
Maximum shearing stress = 65kPa
34. Compute for the value of the confining pressure in kPa.
A. 90
C. 80
B. 70
D. 75
35. What is the cohesion of the soil in kPa?
A. 19.6
C. 18.5
B. 20.2
D. 17.4
36. What is the shearing stress at failure plane, in kPa?
A. 65.35
C. 62.23
B. 68.32
D. 70.45
Situation 13 :
Reservoir B in the figure supplies 560 liters per second to reservoirs A and C. For this
problem, the following data are given :
Pipe 1: D =600 mm, L=500 mm
Pipe 2: D =800 mm, L=800 mm
Pipe 3: D =400 mm, L=800 mm
Assume f= 0.025 for all pipes.
B
A
El. 300
m
Pipe 1
Pipe 2
P
Pipe 3
C
El. 277m
37. What is the flow of pipe in L/s.
A. 132
C. 354
B. 231
D. 179
38. What is the flow in pipe 3 in L/s?
A. 381
C. 302
B. 206
D. 304
39. What is the shearing stress at failure plane, in kPa?
A. 65.35
C. 62.23
B. 68.32
D. 70.45
Situation 14 :
The square footing shown in the figure carries a load of 3500 kN. Assume that the stress
below the footing is distributed at a slope of 1H:2V. The clay layer is overconsolidated with
OCR = 2.
Q = 3500 kN
3m x 3m
0.6 m
Sand; γ=17.7 kN/m3
Sand; γ=18.0 kN/m3
Clay; γ=18.9 kN/m3
GWT
1.2m
mm
Cs =0.05
Cc =0.22
eo =75%
1.2m
mm
40. Determine the effective stress at the midheight of the clay layer, in kPa.
A. 40.45
C. 48.54
B. 43.56
D. 52.12
41. Determine the increase in pressure at the midheight of the clay layer, in kPa.
A. 174
C. 152
B. 198
D. 121
42. Determine the settlement of the overconsolidated clay layer, in mm.
A. 78.3
C. 63.3
B. 69.4
D. 56.74
Situation 15 :
A group of friction piles is shown. The total load on the pile less the soil displaced by the
footing is 1900 kN. L1 = 1.2 m, L2 =1.2 m, L=9m, t=17m, qu=180 kPa, FS=3
43. Compute for the overburden pressure, that is the effective pressure at the midheight of
the consolidating clay layer, in kPa.
A. 123.92
C. 154.98
B. 121.43
D. 132.13
44. Compute for the compression index of the clay.
A. 174
C. 152
B. 198
D. 121
45. What is the approximate settlement of thr foundation?
A. 135mm
C. 102mm
B. 156mm
D. 176mm
Situation 16 :
Given the laboratory results of the attenberg Limits Test. Plot the water content versus the
number of blows.
A. 123.92
C. 154.98
B. 121.43
D. 132.13
46. Determine the nearest value to the liquid Limit of the soil.
A. 49.4%
C. 48.3%
B. 47.1%
D. 46.6%
47. Determine the nearest value to the Plastic Limit of the soil.
A. 38.34
C. 37.49
B. 35.43
D. 39.65
48. Determine the nearest value to the Liquidity Index of the soil.
A. 1.34
C. 1.55
B. 1.87
D. 2.32