Pressure-Depth Relation:

When an object is immersed in a fluid at rest, the fluid exerts pressure on it. The pressure on the object at any point inside the liquid depends on its depth from the free surface of the liquid. It is so since the fluid pressure refers to the weight of the fluid above each square meter at that level.

To find a relation between pressure and depth in a fluid, consider point A which is at the depth h below the free surface of water in a container. We consider a column of fluid over unit area at this point. Therefore, the height of this column is equal to the magnitude of its volume. (This is because volume is equal to the area of cross-section times height, that is, V = a × h. Since we are considering a unit cross-sectional area, a = 1. Thus, V = h.) Now, mass of liquid in this column of unit cross-sectional area can be written as:

Mass = Density × Volume

m = ρ × V

=ρ × h

Therefore, weight of the liquid in this column is : Weight = m × g

= ρ × h × g

where g is the acceleration due to gravity. The value of g is 9.8 m s^{- 2} . Now, the pressure exerted by this column of fluid at point A is the force exerted by the liquid column at point A per unit area.