Question

deduce an expression for the pressure at a depth inside a liquid

Answer 1

pressure, P=(M1L0T1)
height, h=L3
solve using above dimensional formula

Answer 2

Let us consider a container which contains a liquid of density d.

consider a cylindrical column of height h from the surface of liquid of cross section area A.

the volume of liquid column

V=Ax h

mass = density x volume

m= Axhxd

weight w= mxg

w=mg

= Axhxdxg

there are three forces acting on water column.

1. weight, vertically down.

2. force on top surface due to atmospheric pressure ( P°A), acting vertically Down.

3. Force on bottom surface if column due to static pressure of liquid ( PA), acting vertically up

from Newton's law

PA= P° A +w

PA = P° A + hdgA

P= P° + hdg

note : P° read it as p not.