Discussion
A fully developed laminar flow is taking place through a pipe. If the flow velocity is doubled maintaining the flow laminar, the pressure loss would be
Answer: C
The pressure loss is doubled.
For fully developed laminar flow in a pipe, the Hagen-Poiseuille equation gives the pressure drop over length L:
\[ \Delta p = \frac{32\mu L V}{D^{2}} \]
The loss is directly proportional to the average velocity, so doubling V doubles \(\Delta p\). Equivalently, the friction factor f = 64/Re halves as Re doubles while \(V^{2}\) quadruples.
'Halved' and 'unaltered' are wrong. A squared dependence on velocity applies to fully turbulent rough-pipe flow, which would give four times the loss; 'trebled' fits no regime.
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