An engine of mass M pumps water continuously through a hose of cross-sectional area A with speed v. What rate of power must the engine deliver to the water?

Answer and explanation

Correct answer: B. (1/2) ρ A v^3

  1. Step 1: Mass flow rate dm/dt = ρ A v.
  2. Step 2: Kinetic energy imparted per unit time = dK/dt = (1/2) (dm/dt) v^2.
  3. Step 3: Power = (1/2) (ρ A v) v^2 = (1/2) ρ A v^3.

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