Pressure on surfaces immersed in fluid

 1.Total pressure on horizontal surface immersed in fluid-

let, A is the area of the surface

X̄ = Distance between horizontal surface to the fluid surface.

p = Pressure intensity

w = Specific weight of fluid

Pressure intensity (p) = wX̄

Total pressure = Pressure intensity X Area of the surface

So, P= p X A

Since, P = wX̄

So, P= pwX̄   

OR, P = pX̄A

2.Total pressure on vertical surface immersed in fluid-

let the surface is divided into a small and equal surfaces. Whose width is b and thickness is δx. 

The distance between the surface to the main surface is x. And the total distance distance between the vertical surface to the main surface is X̄.

Area of the surface (A) = bδx

Total pressure of the surface, P = p. A

So, P = p. bδx

Since the surface is thin so the pressure intensity will be the same on all surfaces.

So that, P = w. x

so total pressure on the surface

P = p. A

P = wx. bδx

Now total pressure on all the surfaces

= wfx. bδx

But, AX̄ = bδx. fx

Now replace  bδx. fx by AX̄

So 

P = wAX̄

OR 

P = wX̄A