Consider a tiny right-angled triangular prism of liquid of uniform thickness, having its three faces mutually perpendicular and of equal area ΔA. The prism is completely inside a large mass of liquid at rest.
(a) Assuming the pressures on the three mutually perpendicular faces to be P1, P2 and P3 respectively, write the expressions for the normal forces acting on each face.
(b) Using the condition for mechanical equilibrium of the prism, prove that P1=P2=P3.
(c) Hence establish that at a point inside a static fluid the pressure is the same in all directions, and comment on why this result justifies treating pressure as a scalar quantity.