Hydrostatic Forces on Surfaces and Buoyancy Tutorial
1. Determine the total pressure on a circular plate of
diameter 1.5 m which is placed vertically in such a way
that the centre of the plate is 3 m below the free surface
of water. Find the position of the centre of pressure also.
[F = 52002.81 N, h = 3.0468 m]
CP
2. A circular plate 3.0 m in diameter is immersed in water
in such a way that its greatest and least depth below the
free surface are 4 m and 1.5 m respectively. Determine
the total pressure on one face of the plate and the
position of the centre of pressure [F = 190621 N, h =
2.891 m]
CP
3. If in the above question (question 8), the given circular
plate has a concentric circular hole of diameter 1.5 m,
then calculate the total pressure and position of the centre
of pressure on one face of the plate [F = 143.018 kN, h
= 2.927 m]
CP
4. A vertical sluice gate is used to cover an opening in a
dam. The opening is 2 m wide and 1.2 m high. On the
upstream of the gate, the liquid of SG = 1.45, lies up to a
height of 1.5 m above the top of the gate, whereas on the
downstream side, the water is available up to a height
touching the top of the gate. Find the resultant force
acting on the gate and the position of the centre of
pressure. Find also the force acting horizontally at the top
of the gate capable of opening it. Assume that the gate is
hinged at the bottom. [F = 57565 N, h = 0.578 m above
the hinge, F = 27725.5 N]
CP
5. A caisson for closing the entrance to a dry dock is of
trapezoidal form 16 m wide at the top and 10 m wide at
the bottom and 6 m deep. Find the total pressure and
centre of pressure on the caisson if the water on the
outside is just level with the top and the dock is empty [F
= 2.118783 MN, h = 3.833 m]
CP
6. A cubical tank has sides of 1.5 m. It contains water for
the lower 0.6 m depth. The upper remaining part is filled
with oil pf SG = 0.9. calculate for one vertical side of the
tank;
a. Total pressure and [15163.8 N]
b. Position of centre of pressure [1.005 m from A]
7. A rectangular is hinged r gate 5 m x 2 m is hinged at its
base and inclined at 60 to horizontal as shown in the
figure. To keep the gate stable, a counterweight of 500
kgf is attached at the upper end of the gate. Find the
depth of water at which the gate begins to fall. Neglect
the weight of the gate and friction at the hinge and
pulley. [3.83 m]
8. An inverted cone is placed in a water tank as shown. If
the weight of the cone is 16.5 N, what is the tensile force
in the cord connecting the cone to the bottom of the
tank? [20 N]
9. The hull of a boat has a volume of 180 m3, and the total
mass of the boat when empty is 8560 kg. Determine how
much load this boat can carry without sinking
(a) in a lake and [171 500 kg]
(b) in seawater with a specific gravity of 1.03. [176 900
kg]
10. A water tank is being towed on an uphill road that
makes 14° with horizontal with a constant acceleration of
3.5 m/s in the direction of motion. Determine the angle
the free surface of water makes with the horizontal. What
would your answer be if the direction of motion were
downward on the same road with the same acceleration?
[ = 17.7, = -20.8]
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11. A rectangular tank of length 6 m, width 2.5 m and
height 2 m is filled with water when at rest. The tank is
open at the top. The tank is subjected to a horizontal
constant linear acceleration of 2.4 m/s in the direction of
its length. find the volume of water spilled from the tank.
[11.007 m ]
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