(^734) „„„„„ A Textbook of Engineering Mechanics
∴ Depth of centre of pressure of triangular section 1 from the water surface.
h 1 =
3
1
1
11
18 411
(^438)
3
G
ah
I hh
x
Ax h
ah
+= + =
×
Similarly, h^2 =
3
2
2
22
36 551
(^5330)
23
G
ah
I hh
x
Ax ah h
+= + =
×
Now taking the moments about the water surface and equating the same,
13 2
6
wah
×h =
41155122
38 630
⎛⎞⎛⎞wah h wah h
⎜⎟⎜⎟⎜⎟⎜⎟×+ ×
⎝⎠⎝⎠

13 2
4
wah
×h
∴ h = 1.5 h^ Ans.
Example 35.13. A circular plate of diameter 4 metres has a circular hole of 1 metre diameter
with its centre 1 metre above the centre of the plate as shown in Fig. 35.17.
Fig. 35.17.
The plate is immersed in water at an angle of 30º to the horizontal and with its top edge
2 metres below the free surface. Find
(i) the total pressure on the plate, and
(ii) the depth of centre of pressure.
Solution. Given: Diameter of the plate (D) = 4 m; Diameter of the hole (d) = 1 m and
inclination of the plate with the horizontal (θ) = 30º.
Total pressure on the plate
We know that area of the main plate,
A 1 = (4)^224 m
4
π
=π
Similarly, area of hole,
A 2 = (1)^22 0. 25 m
4
π
=π
and depth of centre of gravity of the main plate from the
water surface,
x 1 = 2 + 2 sin 30º = 2 + (2 × 0.5) = 3 m
Similarly, x 2 = 2 + 1 sin 30º = 2 + (1 × 0.5) = 2.5 m
We also know that pressure on the main plate,
P 1 =wA x 11 =×π×=9.8 4 3 369.5 kN
Similarly, P 2 =wA x 22 =× π×=9.8 0.25 2.5 19.2 kN
Fig. 35.18.