Question

Assuming flow to be laminar, if the diameter of the pipe is halved, then the pressure drop will:

• A. \(\text{increase}\)
• B. \(\text{decrease}\)
• C. \(\text{remain same}\)
• D. \(\text{be quadrupled}\)

Hint:

For laminar flow, pressure drop is inversely proportional to \( d^4 \), meaning smaller pipes create much higher pressure drop.

Answer 1

The Correct Option is D

Step 1: Understanding pressure drop in laminar flow. - According to Hagen-Poiseuille equation, pressure drop (\( \Delta P \)) in laminar flow is given by: \[ \Delta P \propto \frac{1}{d^4} \] - If diameter is halved, pressure drop becomes: \[ \left( \frac{1}{(d/2)^4} \right) = 4 \times \Delta P \]
Step 2: Selecting the correct option. Since pressure drop increases fourfold when diameter is halved, the correct answer is (D) be quadrupled.