Variation of Fluid Pressure With Depth
We can think of the pressure exerted by a liquid or gas in the same way. We can imagine a cylinder filled with a fluid of constant density.
The density of the fluid isso the mass of the gas is
The pressure exerted on the base of the cylinder is
This equation is general and does not depend on how the density of fluid varies with height, whether the fluid is a liquid or gas or the cross sectional area of the cylinder.
It is very important to notice also that the pressure at a point in a fluid acts equally in all directions – up down and sideways, so that if an object is inserted in a fluid, the force at any point on the surface of the object will depend only on the pressure and will always be perpendicular to the surface.