(^732) „„„„„ A Textbook of Engineering Mechanics
and depth of centre of gravity of the plate from the water surface,
x =
1.5
2 sin 30º 2 (0.5 0.5) 2.25 m
3
+=+×=
∴ Total pressure on the plate,
P=wA x=× × =9.8 0.75 2.25 16.54 kN Ans.
Centre of pressure
We know that moment of inertia of the triangular section about its centre of gravity and
parallel to the base,
IG=
33
1(1.5) 0.094 m 4
36 36
bh

and depth of centre of pressure from the water surface,
h =
sin^2 0.094 sin 30º^2
2.25 m
0.75 2.25
IG x
Ax
θ ×
+= +
×

0.094 (0.5)^2
2.25 2.264 m
0.75 2.25
+=
×
Ans.
EXERCISE 35.2

1. An isosceles triangular plate of base 3 metres and altitude 3 metres is immersed vertically
   in an oil of specific gravity 0.8 as shown in Fig. 35.15.

Fig. 35.15.

Determine the total pressure and centre of pressure of the plate. [Ans. 35.3 kN; 1.5 m]

2. A square plate of 1 m side is immersed vertically in water, in such a way that its centre is
   4 m below the water surface. Find the total pressure and the position of the centre of
   pressure. Take w as 9.8 kN/m^3 .[Ans. 39.2 kN; 4.02 m]


3. A circular plate of diameter (d) is submerged vertically in water in such a way that its
   centre is (h) below the water surface. Prove that the centre of pressure of the plate is
   2

16

d

h

h

⎛⎞

⎜⎟⎜⎟+

⎝⎠

below the water surface.

4. A square plate 5 m × 5 m hangs in water from one of its corners. The centre of gravity of
   the plate is at a depth of 10 m from the water surface. Find the total pressure on the plate
   and the position of the centre of pressure. [Ans. 2450.5 kN; 10.21 m]


5. A circular plate of 1 m diameter is immersed in water in such a way that its plane makes an
   angle of 30º with the horizontal and its top edge is 1.25 m below the water surface. Find
   the total pressure on the plate and the point, where it acts. Take w as 9.8 kN/m^3.
   [Ans. 11.5 kN; 1.51 m]


6. A rectangular plate 2 m × 1 m is immersed in an oil of specific gravity 0.8. Its plane makes
   an angle of 30º with the oil surface. The 1 m side is parallel to the oil surface and 1.5 m
   below it. Find the total pressure and the depth of centre of pressure from the oil surface.
   [Ans. 31.4 kN; 2.04 m]