Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Laminar and turbulent flow in pipes, Darcy–Weisbach and Hazen–Williams equations
Question Statement:
In a laminar flow regime inside a circular pipe ($Re < 2000$), if the Reynolds number is doubled while maintaining laminar conditions, the Darcy-Weisbach friction factor $f$:
Options:
(A) Is reduced by half ($f' = f / 2$)
(B) Doubles ($f' = 2 f$)
(C) Quadruples ($f' = 4 f$)
(D) Remains unchanged because laminar friction is independent of Reynolds number
Answer Key:
A
Step-by-Step Solution & Explanation
For fully developed laminar flow in a circular conduit, the Darcy friction factor is given by the Hagen-Poiseuille relationship:
$f = \frac{64}{Re}$
If Reynolds number doubles from $Re$ to $2 Re$:
$f' = \frac{64}{2 Re} = \frac{1}{2} \left( \frac{64}{Re} \right) = \frac{f}{2}$
Hence, the friction factor is halved. Option A is correct.