proof:

Suppose a liquid cylinder of volume (VL) in a resting liquid of density (rL).

The cylinder is subjected by 2 forces ………

 i. The horizontal forces in all directions cancel each other.

 ii. The vertical forces :

a) Its weight     WL = mg = rLgVL   ………… (1 

b)      Up thrust force on the cylinder which results from difference in pressure on both bases of the cylinder

P(upper surface)  = Pa + rgh1

 P(lower surface ) = Pa + rgh2

rP = rgh

\ Fb = rP X A  =  rgh X  A

\ Fb = rLgVimmersed ………………………………………… (2)

From 1 & 2

                       Fb = The weight of liquid displaced.