CE 420 – CE Practice with Comprehensive Examinations
SUPPLEMENTARY PROBLEMS (Hydraulics and Principles of Geotechnical Engineering)
SITUATION 1:
Water is contained in an open, 3 m-deep
cylindrical tank that is 2 m in diameter and 4
m height. It rotates with a constant rate of
angular rotation ω about its own vertical axis.
1. What angular speed will just make the depth
of water zero at the center of the tank?
2. What maximum value of angular speed can
be imposed without spilling any liquid?
3. If ω = 100 rpm, how much area at the bottom
of the tank is uncovered?
SITUATION 2:
A cube of timber 0.15 m on each side floats in
water, not fully submerged. The specific
gravity of the timber is 0.75.
4. What is the submerged depth of the cube?
5. What is its draft when it is submerged in
mercury?
6. What downward force is required to keep
the cube fully submerged in water?
SITUATION 3:
A nozzle of 70 mm diameter delivers a stream
of water at a velocity of 55 m/s perpendicular
to a fixed plate.
7. Which of the following most nearly gives
the force on the plate?
8. If the plate moves in the same direction as
the jet at a speed of 15 m/s, which of the
following most nearly gives the force on the
plate?
9. Find also the work done per sec if the plate
moves in the direction of the jet at 15 m/s
SITUATION 4:
Gasoline with a density of ρ=550 kg/m3 at a
depth of 3.75 m is contained on one side of an
open tank with a vertical partition, as
indicated. The divider contains a rectangular
gate with dimensions of 6 m high by 2 m wide
with a hinge at one end.
10. What gives the hydrostatic force acting on
the right side of the gate?
11. If water is slowly added on the empty side
of the tank, at what depth h will the gate start
to open?
12. What gives the hydrostatic force acting on
the left side of the gate?
SITUATION 5:
Assume a specific weight of 10.45 kN/m3 at
the ocean's surface and an average bulk
modulus of elasticity of 2.34 GPa for that
pressure range. The pressure in the ocean at
a depth of 10 km is 82.6 MPa.
13. Determine the change in specific volume
between the surface and 10 km.
14. Determine the specific volume at 10 km.
15. Determine the specific weight at 10 km.
SITUATION 6:
A nine pile group consists of a 0.50 m
diameter friction concrete pile 10 m long. The
piles are driven on clay having an unconfined
compressive strength of 130 kPa and unit
weight of the clay is 15 kN/m3. The spacing of
the piles is 0.75 m center-to-center. Assume
a capacity factor of Nc = 9 and α = 1.0:
16. Find the allowable group pile capacity
based on individual pile failure using a factor
of safety of 3.
17. Find the block capacity of the pile group
based on block failure using a factor of safety
18. Find the minimum pile spacing in order to
achieve a 85% efficiency.
SITUATION 7:
A tri- axial test was conducted on a moist
sand sample. The normal stress and the
shear stress on the failure plane were
determined to be 250 kPa and 200 kPa,
respectively. The cohesion of the soil was
found to be 52.6 kPa.
19. Which of the following most nearly gives
the angle of friction of the soil sample?
20. Determine the angle of the failure plane.
21. What is the minimum principal stress?
SITUATION 8:
The following are the data obtained from the
sieve analysis of a soil sample.
Soil Sample
Sieve
A
B
C
Diameter
No.
Percent
Passing
CE-4202 | CE-4208
Prepared by: Engr. C. M. U. Olano Jr., CE, MP, SO-2
CE 420 – CE Practice with Comprehensive Examinations
SUPPLEMENTARY PROBLEMS (Hydraulics and Principles of Geotechnical Engineering)
4
10
20
40
60
100
200
4.75
2.00
0.850
0.425
0.250
0.150
0.075
100
92
85
50
42
23
10
89
62
44
20
15
9
3
100
98
90
80
79
70
65
22. What gives the effective diameter size of
Soil A in mm?
23. What gives the uniformity coefficient of
Soil A?
24. What gives the coefficient of curvature of
Soil A?
PROBLEM 25:
A cubic meter of soil in its natural state
weighs 18.75 kN. After being dried, it weighs
16.25 kN. Given its specific gravity equal to
2.70, calculate the moisture content of the
soil.
PROBLEM 30:
A soil was found out to have a moist unit
weight of 17.04 kN/m3 at a moisture content of
18%. If the specific gravity of soil solids is 2.7,
how much water (in m3) must be added to a
6.3 m3 of this sample to make it fully
saturated?
“Cast all your anxiety on Him, because He
cares for you.”
-1 Peter 5:7
“AKO NA NEXT” is much better than “SANA
ALL”
PROBLEM 26:
When the moisture content of a soil sample
is 3.45%, the degree of saturation is 18.09%.
What would be its degree of saturation of the
same soil if it has 5.56% water content?
PROBLEM 27:
In a wet soil mass, air occupies 1/6 of its
volume and water occupies 1/3 of its volume.
What is its porosity?
SITUATION 9:
From the figure below:
28. What is the total active force acting on the
retaining wall?
29. Determine the location of the resultant
passive force from the bottom of the retaining
wall.
CE-4202 | CE-4208
Prepared by: Engr. C. M. U. Olano Jr., CE, MP, SO-2