Darcy-Weisbach head loss h_f = f (L/D) (V^2/(2g)). If V doubles, by what factor does h_f change (assuming f constant)?

• A. h_f doubles
• B. h_f increases by a factor of 4
• C. h_f remains the same
• D. h_f changes by a factor of 1/4

Answer: (B)

The head loss from the Darcy-Weisbach equation scales with the square of velocity when the friction factor, length, diameter, and gravity are fixed. So h_f ∝ V^2. If the velocity doubles, V → 2V, and (2V)^2 = 4V^2, meaning h_f becomes four times its original value. Therefore the head loss increases by a factor of four, assuming the friction factor stays constant.