What is the Darcy–Weisbach head loss formula?

• A. h_f = f (L/D) (V^2/(2g))
• B. h_f = (L/D) (V^2/(2g))
• C. h_f = f (D/L) (V^2/(2g))
• D. h_f = f L V /(2gD)

Answer: (A)

The Darcy–Weisbach head loss formula says h_f = f (L/D) (V^2/(2g)). Here, h_f is the loss of energy per unit weight due to friction, f is the dimensionless Darcy friction factor that captures roughness and flow regime, L/D is the length-to-diameter ratio showing how much friction accumulates over the pipe length, and V^2/(2g) is the velocity head, the energy per unit weight associated with the flow speed. Multiplying these together gives the head loss in meters. The other forms either omit the friction factor, invert the length-to-diameter ratio, or mix terms in a way that doesn’t match the standard dimensional form.