Pressure due to liquid column

Let us consider a liquid of density ρ in a vessel as shown in figure. Let us find the pressure difference between two points A and B separated by vertical height h.

To evaluate the pressure difference between A and B, consider an imaginary cubiod of area of cross-section a of liquid with upper and lower cap passing through A and B respectively. The volume of the imaginary cylinder is,.

V=ah

Mass of liquid of imaginary cylinder is,

m = ρah

Let P₁ and P₂ be the pressure on the upper and lower face of cylinder. The different forces acting on the imaginary cylinder are:

(i) weight mg = ρahg in vertically downward direction.

(ii) Downward thrust of F₁ =P₁a on upper cap.

(iii) Upward thrust of F₂ = P₂a on lower face. As the imaginary cylinder in the liquid is in equilibrium, therefore the net force on the cylinder is zero, i.e.

Thus the pressure difference between two points separated vertically by height h in the presence of gravity is ρgh. In the absence of gravity this pressure difference becomes zero.