Topic: Fluid Mechanics
The power transmitted through the nozzle is maximum when the head lost due to friction in the pipe is
- A. Equal to the total supply head
- B. One third of the total supply head
- C. One half of the total supply head
- D. Two third of the total supply head
Answer: B. One third of the total supply head
Explanation: Power transmitted at the outlet of the pipe is evaluated as $P = \rho g Q(H - h_f) = \rho g \frac{\pi}{4}d² V \left(H - \frac{4fLV^2}{d \times 2g}\right)$. For maximum power transmission, the derivative of power with respect to velocity is zero: $\frac{d}{dV}(P) = 0$. Differentiating and solving gives $H - 3 \left(\frac{4fLV^2}{d \times 2g}\right) = 0$, which simplifies to $H - 3h_f = 0$, meaning $h_f = H/3$.