Question

A non–viscous liquid of density 10³ kgm³ has a stream lined flow. PQ is a tube of varying cross–section. The tube is kept in a vertical plane in gravity of earth. The area of cross– section of tube at two points P and Q at height of 2 m and 5 m; as shown in Fig ; is 4 x 10^-3m² and 8 x 10^-3m² respectively. The velocity of liquid at P is 1 ms^-1. What is work done per unit volume by the pressure and the force of gravity as liquid flow from P to Q? (g = 9.8 ms^-2)

Answer 1

Let P₁ , v₁ , h₁ denote liquid pressure; speed of flow and height for end P of cross–sectional area a₁ . The corresponding quantities for end Q are P₂ , v₂ , h₂ and the area of cross–section is a₂ . From equation of continuity

From Bernoulli’s theorem

W₁ = Work done per unit volume by force of pressure = P₁ –P₂

W₂ = Work done by the force of gravity per unit volume