Engineering Mechanics

Chapter 35 : Hydrostatics „„„„„ 721

35.6.TOTAL PRESSURE ON AN IMMERSED SURFACE

As a matter of fact, an immersed surface may be plane, curved or of any geometrical shape.
Moreover, it may be immersed in any way. But a plane surface immersed in the following positions is
important from the subject point of view :

1. horizontal, 2. vertical or 3. inclined.
   Now we shall discuss all the above three cases one by one.

35.7.TOTAL PRESSURE ON A HORIZONTALLY IMMERSED SURFACE

Consider a plane horizontal surface immersed in a liquid as shown
in Fig. 35.3.

Let w = Specific weight of the liquid

A = Area of the immersed surface

x = Depth of the horizontal surface

from the liquid level

We know that the total pressure on the surface,

P = Weight of liquid above the immersed

surface

= Specific weight of liquid × Volume of liquid

= Specific weight of liquid × Area of surface × Depth of liquid

=wAx

Example 35.3. A rectangular tank 5 metres long and 2 metres wide contains water up to a

depth of 2.5 metres. Calculate the pressure on the base of the tank.

Solution. Given: Length of the tank (l) = 5 m; Width of the tank (b) = 2 m and depth of

water (d) = x=2.5 m.

We know that surface area of the base of the tank,

A= 5 × 2 = 10 m^2

and total pressure on the base of the tank

=wAx=××=9.8 10 2.5 245 kN^ Ans.

35.8.TOTAL PRESSURE ON A VERTICALLY IMMERSED SURFACE

Fig. 35.4. Total pressure on a vertical surface.

Consider a plane vertical surface immersed in a liquid as shown in Fig. 35.4.

Let w= Specific weight of the liquid in kN/m^3 ,

A= Area of the immersed surface in m^2 , and

x = Depth of centre of gravity of the surface from the liquid sur-

face in metres

Fig. 35.3. Total pressure on a

horizontal surface.