For a pipe with Darcy friction factor f doubling, how does major head loss h_f change for the same flow?

• A. It remains the same.
• B. It halves.
• C. It doubles.
• D. It quadruples.

Answer: (C)

The major head loss in a pipe is governed by the Darcy–Weisbach relation h_f = f (L/D) (V^2 / 2g). For a fixed pipe length L, diameter D, and the same flow rate (which fixes the velocity V), the only changing term is the friction factor f. This makes h_f scale linearly with f. So if the friction factor doubles, the head loss doubles as well. The other options would require non-linear changes or no change, which isn’t the case here since the dependence on f is direct and proportional.