If velocity doubles in a system with a valve that has loss coefficient K, head loss increases by what factor?

• A. It doubles
• B. It stays the same
• C. It becomes four times as large
• D. It becomes one quarter as large

Answer: (C)

Head loss for a valve scales with the velocity head, which is proportional to v^2. The relationship is Δh = K (v^2 / 2g). If velocity doubles, substitute 2v: Δh' = K ((2v)^2 / 2g) = K (4v^2 / 2g) = 4 Δh. So the head loss becomes four times as large. This holds because the velocity term is squared, and for a fixed valve the loss coefficient K stays the same.