Statement: “In n static fluid the pressure or intensity of pressure at a point is equal in all directions”.

Proof: Let us take a fluid element as shown in Fig. 2.1. BC = dx, AB = d y, AE = d z AC = ds._

P _x = Pressure on ABOE surface

P _y = Pressure on BCDO surface

P _θ= Pressure on ACDE surface

Force on                      ABOE = P _x d _y d _z

Force on                      BCDO = P_Y d_x d _z

Force on                      ACDE = P _θ d _z d_s.

As the fluid element is in equilibrium

Σ F x = 0

or         p _x d _y d _z – p _θ d _z d _S cos e = 0

or                         P _x d _y d _z – P_θ d z d y =0 [ds cos _θ=d y]

or                                                    P x = P_θ

And                                  Σ F_Y =0 [All forces on y direction is zero]

Or               P _y d_x d _z – P _θ d z ds sin _θ = 0

or                           P _y d_x d _z – P_θ dz dx = 0 [ds sin _θ = dx]

or                                                         P y =P _θ

thus                                         P x = PY = P_θ (2.1)

Equation (2.1) is independent of e, therefore it is proved that pressure acts equally in all directions in a stationary fluid.