HYDRAULICS AND PRINCIPLES OF GEOTECHNICAL ENGINEERING

INSTRUCTION: Select the best answer to each of the following questions.

Situation – A water tank has a sloping inclined at 45° with the horizontal. The total depth of water
in the tank is 8m. A water jet issues from an orifice located on an inclined side of the tank under
a hydrostatic head of 5m. or that orifice is located 3 m. vertically above the bottom of the tank.
Coefficient of velocity is 1.0. Neglecting air resistance on the jet.
1. Determine the maximum height of the jet issuing jet arises above the level of the center of orifice
in meters?
A. 1.5 m B. 2.0 m C. 2.5 m D. 3.0 m
2. Determine the time it takes for this particle of the jet to sit the ground that is 1.20 m. below the
bottom of the tank in seconds?
A. 1.77 B. 1.88 C. 1.99 D. 2.10
3. Determine the horizontal distance on the ground traveled by the jet from the center of the orifice
in meters?
A. 16.16 B. 15.16 C. 14.16 D. 13.16
4. A normally consolidated clay located below ground surface has 3 m thickness and void ratio of
1.1.
Uniform load is acting on the ground surface = 40 kPa.
Ave. effective stress at the top of clay = 56 kPa
Ave. effective stress at the midpoint of clay = 80 kPa
Pre-consolidation pressure = 130 kPa
Compression Index = 0.45
Swell Index = 0.06
Compute the primary consolidation settlement in mm.
A. 20 B. 15 C. 150 D. 4
Situation – A The following data were obtained from a field-density test on a compacted fill of
sandy clay. Laboratory moisture density test on the fill material indicated a maximum dry density
of 1924.8 kg/m3 at an optimum water content of 11 percent.
Weight of moist soil removed from test hole = 1038 g
Weight of soil after oven-drying = 914 g
Volume of test hole from rubber-balloon apparatus = 0.000479 m3
5. Determine the water content.
A. 14.5% B. 12.5% C. 13.2% D. 13.6%
6. Determine the dry unit weight of the soil in kN/m3?
A. 18.71 B. 17.25 C. 15.28 D. 16.47
7. Determine the percent compaction of the fill.
A. 99.1 B. 92.8 C. 94.3 D. 98.2
8. A grain-size analysis is performed on 3500g of dry sand from the Cagayan Valley. No soil is
retained on the 12.5-mm openings sieve. A nest of six sieves is subsequently used to separate the
various sand sizes. The openings of the sieve mesh are, from top to bottom; 5,2,1, 0.5, 0.2 and 0.1
mm. The soil masses remaining on each of the six sieves are 217 g, 868 g, 1095 g, 809 g, 444 g, 39
g, and the amount of soil in the bottom pan is 28 g. Determine the effective diameter in mm.
A. 1.69 B. 0.36 C. 1.28 D. 2.65
9. A circular gate 1.5 m. in diameter is inclined at an angle of 45°. Fresh water stands on one side
of the gate to a height of 10 m above the center of the gate. If the gate is hinged at the top, evaluate
the force normal to the gate at the bottom that will require to open it in kN.
A. 87.8 B. 78.8 C. 69.6 D. 96.6
10. A slope of infinite extent is made of dense sand layer at angle of 30 degrees to the horizontal.
Determine the factor of safety of the slope against failure if the angle of internal friction of the soil
is 36 degrees.
A. 1.26 B. 2.34 C. 0.25 D. 1.75
11. A sand cone test was conducted for quality control during compaction of sandy clay. The data
are as follows:
Mass of jar + cone + sand (before use) = 6.08 kg
Mass of jar + cone + sand (after use) = 2.86 kg
Mass of sand to fill the cone = 0.118 kg
Calibrated density of the sand = 1731 kg/m3
Mass of moist soil from hole = 3.34 kg
Moisture content of moist soil = 12.1%
A. 82.9 % B. 88.8 % C. 85.6 % D. 99.8 %
Situation – Given the laboratory results of liquid limit determination by Casagrande’s apparatus
and the Plastic Limit test, determine the following:
12. Determine the nearest value of the Liquid Limit of the soil sample.
A. 52.07% B. 53.26% C. 51.66% D. 52.21%
13. Describe the soil sample based on its degree of plasticity.
A. Medium Plasticity B. Low Plasticity C. Slight Plasticity D. High Plasticity
14. An Atterberg limit test is performed, and the sample results were given (grams):

A. 2.5 B. 2.0 C. 3.5 D. 3.0

15. An underground tunnel is to be constructed at a depth of I0 meters below ground surface for
a subway in Metro Manila. On ground surface and radially located from the line of the tunnel is a
vertical load of 10 MN. Design specifications require that the vertical stress due to the load at the
level of the tunnel should not exceed five (5) percent the vertical stress at the same depth directly
below the load. Obtain the minimum distance, in meters, at which the alignment of the tunnel be
located from the line of application of the load.
Hint: According to the Boussinesq theory, the vertical stress at a point below the surface of a semi-
infinite, homogenous, isotropic soil mass due to a point load Q applied at the ground surface is
given by the equation.
where P = 0.477QN/z^2
N = 1[1 + (r/z)]^2.5
r = horizontal distance oof point from the vertical line of application of the load
z = depth of point below ground surface
A. 13 B. 14 C. 15 D. 16
16. A triaxial shear test was performed on a well – drained sand sample. The normal stress on the
failure plane and the shearing stress on the failure plane were determined to be 63kPa and 42kPa
respectively. Determine the angle, in degrees of the failure plane with respect to the horizontal
plane.
A. 26.2 B. 61.8 C. 54.9 D. 58.7
17. For a certain soil, the cohesion is 50 kPa; the unit weight is 19.2 kN/m 3. Assuming local shear
failure: (Nc = 7.5, Nq =1.80, Ny = 0.48) for local shear failure (Nc = 9, Nq = 2.50, Ny = 1.20) for
general shear failure. Calculate the net ultimate bearing capacity for a strip footing of width 1.25
m and depth of 4.5 m.
A. 411 kPa B. 325 kPa C. 530 kPa D. 444 kPa
18. How many meters of water is equivalent to 2.75 atmospheres?
A. 38.7 m B. 24.8 m C. 31.6 m D. 27.5 m
Situation – After 24 hours of pumping at 50 liters/sec, the water level in an observation well at a
distance of 100 m from the test well is lowered 0.5 m. At another observation well located from
the test well, the water level dropped by 1.0 m.
19. Estimate the rate of flow in cubic meters per day.
A. 4320 B. 4560 C. 4890 D. 5130
20. Evaluate the coefficient of permeability of the aquifer in meters per day.
A. 44.5 B. 20.1 C. 36.3 D. 58.3
21. Compute the transmissibility of the aquifer in square meters per day.
A. 1140 B. 1080 C. 953 D. 1260
22. An unconfined compression test was conducted on a sample of clay having diameter of 50
mm. The failure load was recorded at 250 N. The cohesion strength of the clay, in KPa, is nearest
to a value of.
A. 63.7 B. 127.0 C. 85.2 D. 101.0
Situation – Water flows through an almost level rectangular channel 3 m wide at 12 m^3/sec. The
depth of the channel gradually increases from 1.0 to 1.1 m for length of 5 m.
23. What is the head loss in meters?
A. 0.04 m B. 0.03 m C. 0.02 m D. 0.01 m
24. What is the slope of the energy gradient?
A. 0.002 B. 0.004 C. 0.006 D. 0.008
25. An infinite slope of height 10 m forms an angle of 33 degrees with the horizontal. A laboratory
tests shows that e = 0.557 and Gs = 2.73. If it is subjected to partial seepage that is 5.8 m deep
from the surface of the slope, what is the angle of internal friction of the sand soil for impending
failure?
 A. 41.842 deg B. 26.753 deg C. 39.031 deg D. 50.977 deg
26. Is a material passing No. 200 sieve that is non-plastic, and has a little strength when dry
(PI<4).
A. clay B. silt C. peat D. fine sand
27. Specific weight of liquid.
A. remains constant at every place C. does not vary on any other planet
B. varies from place to place on the earth D. does not remain constant at every place
28. A channel is designed to carry a discharge of 10m3/s and has a slope of 0.005 and roughness
coefficient n=0.014. Determine the depth of the most efficient trapezoidal channel.
A. 1.14 B. 1.25 C. 1.44 D. 1.52
29. An open tank contains 5m deep of liquid having a unit weight of 7kN/m3. Water is poured
over the liquid until the total depth of two liquids is 8m. Evaluate the gage pressure at the interface
in kPa.
A. 35 B. 48 C. 78.5 D. 64.4
30. A block of wood with length “h” and cross – sectional area “A” is submerged in water with
50mm exposed above the water surface. When submerged in a liquid with specific gravity of 1.35,
it will float with 75mm exposed above the liquid surface. If the wood is submerged vertically in a
liquid with specific gravity of 1.03, obtain the length of wood exposed above the surface in mm.
A. 62.1 B. 48.2 C. 52.8 D. 58.9
31. A square footing carries an allowable axial load of 1000 kN kg with its bottom resting on a
ground water table at a depth of 1.5 m below the ground surface. (Nc = 35, Nq = 22, Ny = 19). Take
ρDRY = 17 kN/m3 and ρSAT = 20.5 kN/m3, C = 10 kPa. Determine the dimension of the footing
using a factor of safety of 3.
A. 1.34 B. 1.62 C. 0.96 D. 1.55
Situation - Sphere A is attached to Sphere B by a cable whose mass is negligible. Both spheres are
identical in dimensions, R = 0.6 m, but differ in material composition. If sphere A has a weight of
12 kN and sphere B has a weight of 4 kN and both spheres are thrown in freshwater, determine
the following:
32. The draft of sphere B.
A. 98.5 cm B. 85.8 cm C. 79.5 cm D. 148.6 cm
33. The tension in the cable connecting the spheres.
A. 3241 N B. 3124 N C. 4213 N D. 2134 N
34. The exposed volume of the sphere B in cubic meters.
A. 0.179 B.0.726 C. 0.114 D. 0.220
35. Negative skin friction on piles
 A. is caused due to relative settlement of the soil.
B. is caused in soft clays.
C. decreases the pile capacity.
D. All of the above.
36. The property of a soil which permits water to percolate through it, is called.
A. moisture content B. permeability C. capillarity D. none of these
37. The discharge pipeline of a water system consists of a 5500 m of 300-mm pipe joined by 3660
m of 450-mm pipe that connects to the base of a huge water reservoir. The difference in elevation
between the water surface in the reservoir and the center of the 300-mm pipe at the end of the
line is 45.7 m. Neglecting velocity head and other losses in head due to entrances and using
coefficient of friction of 0.02 for both pipes. Obtain the velocity of the water in the bigger pipeline,
in m/sec.
A. 0.728 B. 0.665 C. 0.443 D. 0.500
38. A right cylindrical container 2.5 m in a diameter is 3 m tall. A 50-mm diameter hole is provided
at the bottom of the container to drain the water when necessary. If it is 2/3 full of water, how
long in minutes does it take to empty the container from the instant that the hole is opened?
Coefficient of velocity and coefficient of contraction both equal to 1.0.
A. 26.61 mins B. 21.16 mins C. 28.83 mins D. 23.38 mins.
Situation - A 6 m clay layer is overlain by a 10 m sand layer. Water table is located 6 m from the
sand ground surface. The saturated unit weight of sand and clay is 18 and 20 kN/m3 respectively.
Dry unit weight of sand is 16 kN/m3. Compression index and void ratio for the clay is 0.45 and
0.8 respectively. To compact the soil, a temporary backfill 3-m high with dry unit weight of 17
kN/m3 is placed on the sand surface.
39. Calculate the degree of consolidation of the clay layer given that a settlement of 50 mm has
already occurred.
A. 55.28 % B. 27.64 % C. 70.70 % D. 35.35 %
40. Calculate the time (days) required for a 50 mm settlement to occur in the clay layer, given that
the coefficient of consolidation is 0.008 m²/day. Consider double drainage for the clay layer.
A. 67.50 B. 110.41 C. 270.01 D. 441.65
Situation - The coefficient of permeability below a dam is 4 m /day. The water on the upstream
side is 20 meters higher than on the downstream side. To estimate the seepage below the dam, a
flow net was graphically drawn such that the number of potential drops, Nd = 10 and the number
of flow channels Nf = 4. The base of the dam is founded 1 m below the ground. Between the heel
and the toe of the dam, a distance of 30 meters, there are 8 potential drops.
41. Evaluate the seepage flow per meter width of dam, in liters/min.
A. 18.5 B. 32.5 C. 20.6 D. 22.2
42. Determine the uplift pressure at the heel of the dam, in kPa.
 A. 114 B. 181 C. 177 D. 198
43. Determine the uplift pressure at the toe of the dam, in kPa.
A. 11.4 B. 19.6 C. 14.7 D. 17.6
Situation – The Air Traffic Control building of an airport is to be founded on a circular mat footing
having a diameter of 10 m. The depth of founding of the footings has to be at 2 m into a soil deposit
of cohesionless soil, for which the angle of internal friction is 20° and the unit weight of which is
16 kN/m3. Using Terzaghi’s formula for general shear failure, bearing capacity constants Nc =
17.69, Nq = 7.44, and Ny = 3.64
44. Evaluate the contribution of the depth of embedment to the ultimate bearing capacity of the
soil, in kPa.
A. 238.1 B. 283.0 C. 220.6 D. 254.3
45. Evaluate the contribution of the footing dimension to the ultimate bearing capacity of the soil,
in kPa.
A. 232.9 B. 174.7 C. 291.2 D. 116.5
46. Evaluate the concentric downward load, in kN, that the footing can safely support, using a
factor of safety of 3.0 against bearing capacity failure.
A. 10,807 B. 12,330 C. 11,982 D. 13,506
Situation – A 3-layer soil has the following properties from top to bottom:

47. Obtain the equivalent horizontal coefficient of permeability, in cm/sec.

A. 0.00689 B. 0.00734 C. 0.00809 D. 0.00747
48. Obtain the equivalent vertical coefficient of permeability, in cm/sec.
A. 0.0000709 B. 0.0000534 C. 0.0000689 D. 0.0000805
49. Estimate the rate of flow in the vertical direction per square meter of layer, in liters/hr, if the
hydraulic gradient is 0.50.
A. 4.65 B. 3.24 C. 1.45 D. 2.85
50. A line joining the points of highest elevation of water in a series of vertical open pipes rising
from a pipeline in which water flows under pressure is referred to as.
A. hydraulic jump B. hydraulic gradient C. hydraulic head D. hydraulic loss