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. 4
• B. 8
• C. 16
• D. 32

Hint:

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.

Answer 1

The Correct Option is B

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)