Water of density \( 1000 \, \text{kg/m}^3 \) is pumped at a volumetric flow rate of \( 3.14 \times 10^{-2} \, \text{m}^3/\text{s} \), through a pipe of inner diameter \( 10 \, \text{cm} \) and length \( 100 \, \text{m} \), from a large Reservoir 1 to another large Reservoir 2 at a height \( 50 \, \text{m} \) above Reservoir 1, as shown in the figure. The flow in the pipe is in the turbulent regime with a Darcy friction factor \( f = 0.06 \), and a kinetic energy correction factor \( \alpha = 1 \). Take \( g = 9.8 \, \text{m/s}^2 \). If all minor losses are negligible, and the pump efficiency is \( 100\% \), the pump power, in \( \text{kW} \), rounded off to 2 decimal places, is:
\includegraphics[width=0.5\linewidth]{q59 CE.PNG}