Question

derive the expression for the variation of pressure with depth​

Answer 1

Answer:

Let the atmospheric pressure be assumed to be Po

If we assume a small ring  at height h from top of the cone, of radius r and thickness dr, 

From geometry, h = 2r

The pressure on this ring would be, P = Po+ρgh

Force on this ring, F = PA

dF = (Po+ρgh)2πrdr

Integrating this force from radius r = 0 to r = H/2

F = ∫0H/2(Po+ρg2r)2πrdr

F = πH2(4Po+3ρgH)