Question

A non - viscous liquid of constant density 1000 kg/m³ flows in a streamline motion along a tube of variable cross section. The tube is kept inclined in the vertical plane as shown in the figure. The area of cross section of the tube at two points P and Q at height of 2 m and 5 m are respectively 4 x 10^-3 m² and 8 x 10^-3 m². The velocity of the liquid at point P is 1 m/s. Find the work done per unit volume by the pressure and the gravity forces as the fluid flows from point P to Q. Take g = 9.8 m/s².

Answer 1

From continuity equation, we have

Applying Bernoulli's equation at section 1 and 2

(i) Work done per unit volume by the pressure as the fluid flows from P to Q

(ii) Work done per unit volume by the gravity as the fluid flows from P to Q