How does head loss change with pipe length in fully developed flow?

• A. Head loss increases proportionally with length; doubling L doubles h_f.
• B. Head loss increases with length squared.
• C. Head loss independent of length.
• D. Head loss decreases with length.

Answer: (A)

The main idea is that friction head loss accumulates linearly with pipe length in fully developed flow. In the Darcy–Weisbach relation, h_f = f (L/D) (V^2 / 2g), the loss scales with L. If you keep the diameter and the flow rate (hence velocity) fixed, and the friction factor f stays about the same for that regime, then h_f increases in direct proportion to L. So doubling the pipe length doubles the head loss. The per-unit-length loss h_f/L is constant under those conditions, which explains the linear relationship. If you change flow rate or diameter, the exact amount changes, but the linear dependence on length remains as long as the flow regime doesn’t change.