Engineering Mechanics

(^740) „„„„„ A Textbook of Engineering Mechanics
EXERCISE 35.5

1. A hollow circular plate of 2 m exteral diameter and 1 m internal diameter is immersed
   vertically in water, such that centres of the plate is 2 m deep from the water surface. Find
   the total pressure and the depth of centre of pressure.
   [Ans. 46.3 kN; 2.16 m]


2. A composite section is made up of a rectangle 4 m × 2 m and a triangle of base 2 m and
   height 3 m. The base of the triangle is connected to the 2 m side of the rectangle. The plate
   is immersed in water at an angle of 30º with the horizontal, in such a way that the rectan-
   gular portion is above the triangular one and its 2 m side is parallel to the water surface
   and 1 m below it.
   Find the total pressure on the plate and the position of the centre of the plate.
   [Ans. 260.0 kN; 2.71 m]

QUESTIONS

1. What do you understand by the term hydrostatic pressure?


2. Derive an equation for the total pressure on a vertical immersed surface.


3. Define total pressure on a surface and centre of pressure of a surface.


4. From the first principles, derive a relation for the centre of pressure on a vertical immersed
   surface.


5. Show that the centre of pressure of a body is always below its centre of gravity.


6. Derive an expression for the depth of centre of pressure of an inclined surface immersed
   in a liquid.


7. Explain the uses of pressure diagram in hydrostatics.

OBJECTIVE TYPE QUESTIONS

1. The total pressure on a horizontally immersed surface is
   (a) wA (b) wx
   (c) wA x (d) wA x^2
   where w= Specific weight of the liquid,
   A= Area of the immersed surface, and
   x = Depth of centre of gravity of the immersed surface from the
   liquid surface.


2. The intensity of pressure on an immersed surface ...... with the increases in its depth from
   the liquid surface.
   (a) Increases (b) Does not change (c) Decreases


3. The centre of pressure of an immersed surface acts ...... its centre of gravity,
   (a) Above (b)At (c) Below


4. The depth of centre of pressure (h) of a vertically immersed surface from the liquid
   surface is given by

(a) –

IG x

Ax (b)

G –

I

Ax

x

(c)

G

Ax

x

I

+ (d) G

I

x

Ax

+