A high-pressure homogenizer pumps fluid milk at a volumetric flow rate of $3600\text{ L/h}$ ($0.001\text{ m}^3\text{/s}$) against an operating homogenization pressure differential of $20.0\text{ MPa}$ ($2.0 \times 10^7\text{ Pa}$). If the mechanical efficiency of the homogenizer drive is $80\%$, the electric power required to drive the homogenizer in $\text{kW}$ is ________ (answer in integer).
Answer Key:
25
Step-by-Step Solution & Explanation
1. Hydraulic power output $P_h$:
$P_h = Q \cdot \Delta P = 0.001\text{ m}^3\text{/s} \times 20.0 \times 10^6\text{ Pa} = 20000\text{ W} = 20.0\text{ kW}$
2. Shaft electric power input $P$:
$P = \frac{P_h}{\eta} = \frac{20.0\text{ kW}}{0.80} = 25.0\text{ kW}$