Fluid Statics
Example 5:

A vertical gate of height H and width B held water to its one side up to the top level. If the plate is divided by N such lines that the total force on each plate is equal then show that a) the height of the each portion is given by h=Hv(r/N) and b) the depth of centre of pressure of each portion is given by h p = (2/3)H[r 3/2 - (r-1) 3/2 ] / vN

Solution :

a)          Let, the forces on each plate be F 1, F 2, F 3  etc.
                             
            Thus we have
                           
                         

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