Hazen–Williams head loss formula and typical validity range?

• A. h_f = 10.67 L Q^1.852 /(C^1.852 D^4.871); valid for water at ~20°C in metallic or lined pipes, moderate Re
• B. h_f = 10.67 L Q^1.852 /(C^2 D^4.871)
• C. h_f = 20.0 L Q^1.852 /(C^1.852 D^4.871)
• D. h_f = 10.67 L Q^1.852 /(C^1.852 D^5.000)

Answer: (A)

The main idea is that Hazen–Williams gives head loss from friction in a pipe as an empirical relation that ties together how long the pipe is, how much water is flowing, and how large and smooth the pipe interior is. The accepted form is hf = 10.67 × L × Q^1.852 / (C^1.852 × D^4.871). Here L is the pipe length in feet, Q is the flow in cubic feet per second, and D is the pipe diameter in inches. The constant 10.67 comes from the unit system, so this version is for customary units.

The way the variables influence head loss is intuitive: doubling the length doubles hf, increasing the flow raises hf quite strongly (about Q^1.852), increasing the diameter reduces hf sharply (D^4.871 in the denominator), and increasing the roughness coefficient C (a rougher interior means a smaller C) increases head loss since C appears in the denominator raised to 1.852. A higher C means a smoother interior and less friction loss.

This formula is valid for water around 20°C flowing full in metallic or lined pipes where the flow is fully developed and turbulent (moderate Reynolds numbers). It is not appropriate for very rough pipes, very nonuniform or non-water fluids, or conditions far from the calibrated range (in those cases, Darcy–Weisbach or other methods are preferred).