An incompressible fluid is flowing through a tube of uniform cross-section. The increase in the power of the pump required to double the rate of flow is:
Show Hint
- 200\%
- 100\%
- 700\%
- 800\%
The Correct Option is C
Solution and Explanation
Step 1: Understanding the Power-Flow Rate Relationship
- Power \( P \) required to maintain the flow of an incompressible fluid is given by: \[ P \propto Q^3 \] where \( Q \) is the volumetric flow rate.
Step 2: Effect of Doubling Flow Rate
- If the flow rate is doubled: \[ Q' = 2Q \] - New power required: \[ P' = (2Q)^3 = 8P \]
Step 3: Increase in Power
\[ \text{Increase in power} = P' - P = 8P - P = 7P \] \[ \text{Percentage increase} = \frac{7P}{P} \times 100 = 700\% \]
Step 4: Conclusion
Since the power increase is 700\%, Option (3) is correct.
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