Question:
A pump is used to deliver water at a certain rate from a given pipe. To obtain twice the volume of water from the same pipe in the same time, by what factor must the power of the motor pump be increased?
A pump is used to deliver water at a certain rate from a given pipe. To obtain twice the volume of water from the same pipe in the same time, by what factor must the power of the motor pump be increased?
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Volume flow rate $Q \propto v$. Power $P \propto Q \cdot v^2$, so $P \propto v^3$. If velocity doubles, power increases $2^3 = 8$ times.
Updated On: May 5, 2026
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The Correct Option is B
Solution and Explanation
Step 1: Concept
Power for a flowing fluid is proportional to the cube of the velocity ($P \propto v^3$).
Step 2: Meaning
Doubling the volume of water in the same time means doubling the flow rate, which requires doubling the velocity ($v' = 2v$).
Step 3: Analysis
Since $P \propto v^3$, the new power $P' \propto (2v)^3 = 8v^3$.
Step 4: Conclusion
The power must be increased by a factor of 8.
Final Answer: (B)
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