Variation of Pressure with Depth

Let us learn about Variation of Pressure with Depth.
Consider a fluid at rest in a container. In Fig. point 1 is at height h above a point 2.
The pressures at points 1 and 2 are P1 and P2 respectively. Consider a cylindrical element of
fluid having area of base A and height h. As the fluid is at rest the resultant horizontal forces
should be zero and the resultant vertical forces should balance the weight of the element. The
forces acting in the vertical direction are due to the fluid pressure at the top (P1A) acting
downward, at the bottom (P2A) acting upward. If mg is weight of the fluid in the cylinder we
have (P2 − P1) A = mg
Now, if ρ is the mass density of the fluid, we have the mass of fluid to be m = ρV= ρhA so
that
P2 − P1= ρgh
Fluid under gravity. The effect of gravity is illustrated through pressure on a vertical
cylindrical column.

Pressure difference depends on the vertical distance h between the points (1 and 2), mass
density of the fluid ρ and acceleration due to gravity g. If the point 1 under discussion is
shifted to the top of the fluid (say water), which is open to the atmosphere, P1 may be replaced
by atmospheric pressure (Pa) and we replace P2 by P. Then Eq. gives
P = Pa + ρgh
Thus, the pressure P, at depth below the surface of a liquid open to the atmosphere is
greater than atmospheric pressure by an amount ρgh. The excess of pressure, P − Pa, at
depth h is called a gauge pressure at that point.
Hope the above explains about Variation of Pressure with Depth, now let me explain about Vapour pressure.