Question

Consider the fully-developed flow of a Newtonian fluid (density \( \rho \); viscosity \( \mu \)) through a smooth pipe of diameter \( D \) and length \( L \). The average velocity of the flow is \( V \). If the length of the pipe is doubled, keeping \( V \), \( D \), \( \rho \), \( \mu \) constant, the friction factor

• A. increases by two times
• B. remains the same
• C. decreases by two times
• D. increases four times

Hint:

The friction factor in fully-developed flow through a smooth pipe does not depend on the pipe length, but rather on the Reynolds number and the pipe roughness.

Answer 1

The Correct Option is B

For fully-developed flow in a smooth pipe, the friction factor \( f \) depends on the Reynolds number and is independent of the pipe length. The Darcy-Weisbach equation describes the pressure drop in a pipe as: \[ \Delta P = f \frac{L}{D} \frac{\rho V^2}{2} \] Here, the friction factor \( f \) is related to the flow characteristics (like Reynolds number), but it does not depend on the length of the pipe \( L \). Since all other variables are held constant, doubling the pipe length \( L \) will not change the friction factor. Therefore, the friction factor remains the same. The correct answer is (B).
Final Answer: (B) remains the same