Question

Calculate the power required for homogenizer if flow rate is 10,000 lph and homogenizing pressure is 250 bar.

• A. 50 kW
• B. 56 kW
• C. 90 kW
• D. 70 kW

Hint:

To quickly calculate homogenizer power in kW, use the formula:
\[ P \text{ (kW)} \approx \frac{\text{Flow (lph)} \times \text{Pressure (bar)}}{36,000} \]
Applying this here:
\[ P = \frac{10,000 \times 255}{36,000} \approx 69.4\text{ kW} \rightarrow 70\text{ kW} \]

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
A homogenizer is a high-pressure pump that forces a fluid through a narrow valve to reduce the size of suspended particles or droplets.
The mechanical power required to drive this process depends directly on the volumetric flow rate and the pressure difference generated across the valve.
Key Formula or Approach:
The fluid power required is calculated as:
\[ \text{Power } (P) = Q \times \Delta p \]
where:
\( Q \) is the volumetric flow rate in \( \text{m}^3\text{/s} \),
\( \Delta p \) is the pressure in Pascals (\( \text{Pa} \)).

Step 2: Detailed Explanation:
Let us convert the given values into SI units:
Flow rate, \( Q = 10,000\text{ lph} \)
\[ Q = \frac{10,000 \times 10^{-3}\text{ m}^3}{3600\text{ s}} = \frac{10}{3600}\text{ m}^3\text{/s} = \frac{1}{360}\text{ m}^3\text{/s} \]
Pressure, \( \Delta p = 250\text{ bar} \)
Since \( 1\text{ bar} = 10^5\text{ Pa} \):
\[ \Delta p = 250 \times 10^5\text{ Pa} = 2.5 \times 10^7\text{ Pa} \]
Substitute these values into the power equation:
\[ P = \frac{1}{360} \times 2.5 \times 10^7\text{ W} \]
\[ P = \frac{25,000,000}{360}\text{ W} \approx 69,444.4\text{ W} = 69.44\text{ kW} \]
Rounding to the nearest standard motor rating option, we get \( 70\text{ kW} \).

Step 3: Final Answer:
The power required for the homogenizer is \( 70\text{ kW} \).