Discussion
Water is flowing in two different tubes of diameters D and 2D, with the same velocity. The ratio of laminar friction factors for the larger diameter tube to the smaller diameter tube is
Answer: A
The ratio is 0.5.
For laminar pipe flow the Darcy friction factor is \(f = 64/Re\), with \(Re = \rho V D/\mu\). At the same velocity and fluid, doubling the diameter doubles Re, so f halves:
\[ \frac{f_{2D}}{f_{D}} = \frac{Re_{D}}{Re_{2D}} = \frac{1}{2} \]
A ratio of 1.0 would mean f does not depend on Re, which is true only in fully rough turbulent flow, not laminar. 2.0 and 4.0 invert the dependence.
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