Topic: Fluid Mechanics
Water at $25^{\circ}C$ is flowing through a 1.0 km long GI pipe of 200 mm diameter at the rate of 0.07 $m³/s$. If value of Darcy friction factor for this pipe is 0.02 and density of water is 1000 $kg/m³$, the pumping power (in kW) required to maintain the flow is
- A. 1.8
- B. 17.4
- C. 20.5
- D. 41.0
Answer: B. 17.4
Explanation: The head loss due to friction is given by $h_f = \frac{f L Q²}{12 D^5} = \frac{0.02 \times 1000 \times (0.07)^2}{12 \times (0.2)^5} = 25.52$ m. The required pumping power is calculated as $P = \rho g Q h_f = 1000 \times 9.81 \times 0.07 \times 25.52 = 17524.58$ W, which is approximately 17.4 kW.