Engineering Mechanics

Chapter 35 : Hydrostatics „„„„„ 731

Total pressure on one face of the plate
Let θ = Inclination of the plate with the water surface

∴ sin θ =

2–1 1

33

=

We know that area of the circular plate,

A = ()^22 (3) 2.25 m^2

44

d

ππ

==π

and depth of centre of gravity from the water surface,

x =

12

1.5 m

2

+

=

∴ Total pressure on one face of the plate,

P =wA x=× π×9.8 2.25 1.5 kN

= 103.9 kN Ans.

Position of the centre of pressure

We know that moment of inertia of a circular plate, about its centre of gravity,

IG=

()44 4(3)^81 m

64 64 64

d

ππ π

==

∴ Depth of centre of pressure from the water surface,

h =

2

2

81 1

sin 64 3

1.5

2.25 1.5

IG x

Ax

π ⎛⎞

×⎜⎟

θ ⎝⎠

+= +

π×

= 1.54 m Ans.

Example 35.11. A triangular plate of 1 m base and 1.5 m altitude is immersed in water. The
plane of the plate is inclined at 30º with water surface, while the base is parallel to and at a depth of
2 m from the water surface as shown in the figure given below.

Fig. 35.14.
Find the total pressure on the plate and the centre of pressure.
Solution. Given: Base of the plate (b) = 1 m; Altitude of the plate (h) = 1.5 m and inclination
of the plate with the water surface (θ) = 30º.

Total pressure on the plate

We know that area of the triangular plate,

A=

11.50.75 m 2

22

bh ×

==

Fig. 35.13.