Engineering Mechanics

Chapter 35 : Hydrostatics „„„„„ 725

But ∫ lb dx = Moment of the surface area about O

=

sin

Ax

θ

∴ P = sin sin

Ax
w θ×
θ
=wax ...(Same as in Art. 35.7 and 35.8)
Example 35.7. A triangular plate of 1 metre base and 1.5 metre altitude is immersed in
water. The plane of the plate is inclined at 30° to the free surface of water, and the base is parallel to
and at a depth of 2 metres from water surface. Find the total pressure on the plate.

Solution. Given: Base of plate (b) = 1 m; Altitude of plate (h) = 1.5 m and indination
of the plate with the free surface of water (θ) = 30°.

Fig. 35.8.

We know that area of the triangular plate,

A =^2

11.5

0.75 m

22

bh ×

==

and depth of the centre of gravity of the plate from the water surface,

x =

1.5

2sin30º

3

+ = 2 + 0.5 × 0.5 = 2.25 m

∴ Total pressure on the plate,

P=wA x=× ×9.8 0.75 2.25 kN= 16.54 kN Ans.

EXERCISE 35.1

1. A tank 10 m × 10 m contains water up to a height of 1.5 metres. Determine the intensity
   of pressure and total pressure on the bottom of the tank. [Ans. 14.7 kN/m^2 ; 1470 kN]


2. A circular plate of 1.2 m diameter is immersed vertically in water, in such a way that its centre
   is 3 m below the water surface. Find the total pressure on the plate. [Ans. 33.3 kN]


3. A horizontal passage 4 m × 4 m has its outlet covered by a plane flap inclined at 60º with the
   horizontal, and is hinged along the upper horizontal edge of the passage. If the depth of the
   flowing water is 0.5 m in the passage, find the thrust on the gate. [Ans. 2.26 kN]

35.10.CENTRE OF PRESSURE

We have discussed in Art. 35.2 that the intensity of pressure, on an immersed surface, is not
uniform; but increases with the depth. As the pressure is more over the lower portion of the figure,
therefore resultant pressure, on an immersed surface, will act at some point, below the centre of