1. An open cylindrical vessel having a height equal to its diameter is half-filled with water and
revolved about its own vertical axis with a constant angular speed of 125 rpm. Find its minimum
diameter so that there can be no liquid spilled.
2. Determine the stress at the walls of a 250 mm diameter pipe, 12.5 mm thick under a pressure of
170 m of water and submerged to a depth of 125 m in salt water.
3. An open manometer attached to a pipe shows a deflection of 150 mmHg with the lower level of
mercury 450 mm below the centerline of the pipe carrying water. Calculate the pressure at the
centerline of the pipe
4. Distilled water stands in a glass tube of 7.5 mm diameter at height of 24 mm. What is the true
static height? Use σ = 0.0842 N/m.
5. Two large plane surfaces are 30 mm apart and the space between them is filled with a liquid of
viscosity, µ = 0.960 Pa-s. Assuming the velocity gradient to be a straight line, what force is required
to pull a very thin plate of 0.37 m2 area at constant speed of 0.25 m/s if the plate is 10.25 mm
from one of the surfaces?
6. The semi-circular gate shown is hinged at B. Determine the force F required to hold the gate in
position.
7. A 1.85 m diameter closed cylinder, 2.95 m high is filled with oil having sg = 0.80 under a pressure
of 6.5 kg/cm2 at the top. (a) What angular speed can be imposed on the cylinder so that the
maximum pressure at the bottom of the tank is 12.5 kg/cm2 (b) compute the pressure force
exerted by oil on the side of the tank in kg.
8. The funnel shown in the figure is full of water. The volume of the upper part is 90 liters and the
lower part is 74 liters. What is the force tending to push the plug out?
9. An atomizer forms water droplet 50 µm in diameter. Determine the excess pressure within these
droplets using σ = 0.0725 N/m.
10. A hollow cylinder 1 m in diameter and 2 m high weighs 3 900 N. (a) How many kN of lead weighing
125 kN/m3 must be fastened to the outside bottom of the cylinder to make it float with 1.5m
submerged in water (b) How many kN of lead if it is placed inside the cylinder?
11. The pressure at point m in the figure shown was increased from 80 kPa to 115 kPa. This causes
the top level of mercury to move 20 mm in the sloping tube. What is the inclination, ϴ?
12. In the figure shown find the width b of the concrete dam necessary to prevent the dam from
sliding. The specific gravity of concrete is 2.4 and the coefficient of friction between the base of
the dam and the foundation is 0.4. Use 1.5 as the factor of safety against sliding. Is the dam also
safe from overturning?
13. A cylindrical buoy 625 mm in diameter and 1.8 m high weighs 225 kg. It is moored in salt water to
a 12.5 m length of chain weighing 12 kg per m of its length. At high tide, the height of buoy
protruding above water surface is 0.84. What could be the length of protrusion of the buoy if the
tide dropped 2.1 m Density of steel is 7 790 kg/m3. Use density of water = 1000 kg/m3.
14. In the figure shown, determine the difference in pressure between points A and B.
15. A vertical cylindrical tank, open at the top, is filled with a liquid. Its sides are held in position by
means of two steel hoops, one at the top and the other at the bottom. Determine the ratio of the
stress in the upper hoop to that in the lower hoop.
16. A vertical rectangular gate 2.0 m wide and 4.0 m high is submerged in water with its top edge 2
m below the water surface. Find the total pressure acting on one side of the gate and its location
from the bottom.
17. The wooden beam of (sg = 0.64) is 125 mm by 125 mm and is hinged at A, as shown in the figure
below. At what angle ϴ will the beam float in water?
18. The isosceles triangle gate shown in the figure is hinged at A and weighs 1250 N. What is the total
hydrostatic force acting on one side of the gate in kN?
19. In the figure shown, the deflection of mercury is initially 250 mm. If the pressure at A is increased
by 50 kPa, while maintaining the pressure at B constant, what will be the new mercury deflection?
20. The 1.5m diameter impeller of a closed centrifugal water pump is rotated at 1500 rpm. If the
casting is full of water, what pressure is developed by rotation?
21. A differential manometer is attached to a pipe as shown. Calculate the pressure difference
between points A and B.
22. An open cylindrical tank if 1.95 m2 cross-sectional area and 3.25 m high contains 3000 liters of
water. Into it is lowered another smaller tank of the same height but of 0.93 m2 cross-section in
the inverted position, allowing its open end to rest on the bottom of the bigger tank. Determine
the maximum tension per vertical millimeters on the sides of the bigger tank. Neglect thickness
of the metal forming the inner tank and assume normal barometric pressure.
23. A cube 2.2 feet on an edge has its lower half of sg = 1.6 and upper half of sg = 0.7. It rests in a twolayer fluid, with lower sg = 1.4 and upper sg = 0.8, Determine the height h of the top of the cube
as shown
24. A block of wood 0.60 m x 0.60 m x h meters in dimension was thrown into the water and floats
with 0.18 m projecting above the water surface. The same block was thrown into a container of a
liquid having a specific gravity of 0.90 and it floats with 0.14 m projecting above the surface.
Determine the following: (a) The value of h; (b) The specific gravity of the block, and ; (c) The
weight of the block
25. Find the angle the surface tension film leaves the glass for a vertical tube immersed in water if the
diameter is 0.25 inch and the capillary rise is 0.08 inch. Use σ = 0.005 lb./ft
26. Compute the barometric pressure in kPa at an altitude of 1 350 m if the pressure at sea level is
101.3 kPa. Assume isothermal conditions a 21°C. Use R=287 Joule/kg-°K.
27. The 2.00 m diameter impeller of a closed centrifugal water pump is rotated at 2200 rpm. If the
casting is full of water, what pressure is developed by rotation?
28. A 2.0 m diameter closed cylinder, 2.25 m high is filled with glycerin having sg = 1.6 under a
pressure of 245 kPa at the top. The steel plates form the cylinder are 5 mm thick with an ultimate
tensile stress of 82 MPa. How fast can it be rotated about its vertical axis to the point of bursting?
29. Two clean parallel glass plates, separated by a distance d=1.5 mm, are dipped in a bath of water.
How far does the water rise due to capillary action, if σ = 0.0730 N/m?
30. A vessel containing oil is accelerated on a plane inclined 17.5° with the horizontal at 1.5 m/s2.
Determine the inclination of the oil surface when the motion is (a) upwards, and (b) downwards.
31. A closed rectangular tank 4.5 m long, 2.5 m wide, and 2.5 m high is filled with water to a depth of
1.8 m. If the allowable force at the rear wall of the tank is 200 kN, how fast can it be accelerated
horizontally?
32. A vertical rectangular gate 2.5m wide and 1.25 m high has a water in one side with surface 3 m
above its top. Determine the magnitude of the total hydrostatic force acting on the gate and its
distance from the water surface.
33. In the figure shown, if the atmospheric pressure is 101.03 kPa and the absolute pressure at the
bottom of the tank is 231.3 kPa, what is the specific gravity of olive oil?
34. In the figure shown, stop B will break if the force on it reaches 50 kN Find the critical water depth.
The length of the gate perpendicular to the sketch is 1.5m.
35. If air had a constant specific weight of 12.2 N/m2 and were incompressible, what would be the
height of the atmosphere if the atmospheric pressure (sea level) is 102 kPa.
36. A wooden storage vat is 6 m in diameter and is filled with 8 m of oil, s = 0.80. The wood staves are
bound by flat steel bands, 50 mm wide by 6.25 mm thick whose allowable tensile stress is 110
MPa. What is the required spacing of the bands near the bottom of the vat, neglecting any initial
stress?
37. A right circular cone is 125 mm in diameter and 250 mm high and weighs 1.75 N in air. How much
force is required to push the cone (vertex downward) into a body of liquid having sg = 0.80, so
that its base is exactly at the surface? How much additional force is required to push the base 10
mm below the surface?
38. A spherical balloon, 9.25 m in diameter is filled with helium gas pressurized to 111 kPa at a
temperature of 20°C and anchored by a rope to the ground. Neglecting the dead weight of the
balloon, determine the tension in the rope Use R = 212 m/°K for helium gas and = 11.76 / .
39. A vertical cylindrical tank with a diameter of 12.5 m and a depth of 4 m is filled with water to the
top with water at 20°C. If the water is heated to 50°C, how much water will spill over? Unit weight
of water at 20°C and 50°C is 9.79 kN/m3 and 9.69 kN/m3 respectively.
40. A closed cylindrical vessel, 3m in diameter and 4m high is filled with water to a depth of 3m and
rotated about its own vertical axis at a constant angular speed, ω. The air inside the vessel is under
a pressure of 120 kPa. (a) if ω=12rad/sec, what is the pressure at the center and circumference at
the bottom of the tank? (b) what angular speed ω will just zero the depth of water at the center?
(c) if ω = 20 rad/sec how much area at the bottom is uncovered?