Section 4: Soil and Water Conservation Engineering
Pipe Flow, Darcy-Weisbach & Minor Losses
Subtopic: Laminar flow friction factor vs Reynolds number
Question Statement:
For fully developed laminar flow of a Newtonian fluid through a smooth circular pipe of diameter $D$ at Reynolds number $Re$, the Darcy friction factor $f$ is given by:
Options:
(A) $f = \frac{64}{Re}$
(B) $f = \frac{16}{Re}$
(C) $f = \frac{0.316}{Re^{0.25}}$
(D) $f = \frac{0.079}{Re^{0.25}}$
Answer Key:
A
Step-by-Step Solution & Explanation
In Hagen-Poiseuille laminar pipe flow, the pressure drop is $\Delta P = \frac{32 \mu v L}{D^2}$. Equating this with the Darcy-Weisbach form $\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}$ yields:
$f = \frac{64 \mu}{\rho v D} = \frac{64}{Re}$
Note: Fanning friction factor $f' = 16/Re$, but the standard engineering Darcy friction factor is $64/Re$.