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.