Question

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:

• A. 200\%
• B. 100\%
• C. 700\%
• D. 800\%

Hint:

For an incompressible fluid in a uniform tube, power required to maintain the flow is proportional to the cube of the flow rate.

Answer 1

The Correct Option is C

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.