Question Detail
Question
A non-viscous liquid of constant density ρ 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 heights of h₁ and h₂ are respectively A₁ and A₂. The velocity of the liquid at point P is v₁. Find the work done on a small volume ΔV of fluid by the neighbouring fluid as the small volume moves from P to Q.
Correct Answer
Option B is the correct answer.
Detailed Explanation
Using Bernoulli's equation and the work-energy theorem, the work done by neighboring fluid equals the change in kinetic energy plus change in potential energy. With continuity equation A₁v₁ = A₂v₂, v₂ = (A₁/A₂)v₁. So change in KE = ½ρΔV(v₂² - v₁²) = ½ρΔV[(A₁²/A₂²)v₁² - v₁²] = ½ρΔV(A₁²/A₂² - 1)v₁². Change in PE = ρΔVg(h₂ - h₁). Therefore total work = ½ρΔV(A₁²/A₂² - 1)v₁² + ρΔVg(h₂ - h₁).
Hint
Apply Bernoulli's equation and continuity equation.