Question

Describe an experimental proof of Pascal’s law.

Answer 1

Consider a spherical vessel having four cylindrical tubes A, B, C and D each fitted with air-tight

frictionless pistons of areas of cross section A, A/2, 2A and 3A, respectively, as shown in above figure. The vessel is filled with an incompressible liquid such that there is no air between the liquid and the pistons.

If the piston A is pushed with a force F, the pressure on the piston and the liquid in the vessel is p_A = F/A. It is seen that the other three pistons are pushed outwards. To keep these pistons at their respective original positions, forces of F/2, IF and 3F, respectively are required to be applied on pistons B, C and D respectively to hold them. Then, the pressures on the respective pistons are

P_B = \(\frac{F/2}{A/2}\) = F/A, P_C= 2F/2A = F/A and

p_D = 3F/3A = F/A 

∴ p_A = p_B = p_C = p_D = F/A

This indicates that the pressure applied is trans-mitted equally to all parts of liquid. This proves Pascal law.