Question Bank • QB_DFE_EXP_026 NAT • 2 Marks

Section 7: Dairy and Food Engineering

Unit Operations in Dairy and Food Engineering

Subtopic: Homogenization

Question Statement:

In a dairy homogenizer, $2500\text{ L/h}$ ($0.000694\text{ m}^3\text{/s}$) of milk is pumped through the homogenizing valve under a total pressure drop of $20.0\text{ MPa}$ ($200\text{ bar}$). If the mechanical efficiency of the homogenizer pump is $80\%$, the electric power required in $\text{kW}$ is ________ (round off to 2 decimal places).

Answer Key:

17.36

Step-by-Step Solution & Explanation

1. Hydraulic power $P_h = Q \times \Delta P$: $Q = \frac{2500 \times 10^{-3}\text{ m}^3}{3600\text{ s}} \approx 6.9444 \times 10^{-4}\text{ m}^3\text{/s}$ $\Delta P = 20.0 \times 10^6\text{ Pa}$ $P_h = (6.9444 \times 10^{-4}) \times (20.0 \times 10^6) = 13,888.9\text{ W} = 13.889\text{ kW}$ 2. Electric power input $P_{el} = \frac{P_h}{\eta}$: $P_{el} = \frac{13.889\text{ kW}}{0.80} \approx 17.361\text{ kW} \approx 17.36\text{ kW}$
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