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The Hazen-Williams formula relates flow rate to pipe diameter, length, friction coefficient C, and head loss. It is the standard method for pressurized water distribution in building plumbing.
Q = 0.442 × C × D^2.63 × S^0.54 (Q in GPM, D in inches, S = head loss ft/ft)Convert available pressure (psi) to head (feet of water) and divide by pipe length to get the friction slope S used in the equation.
Head (ft) = PSI × 2.31; S = Head / Pipe length (ft)Verify flow velocity stays within recommended limits: 2–4 fps for domestic hot water, 4–8 fps for cold supply mains, and below 5 fps to minimize noise and erosion.
Velocity (fps) = 0.408 × Q / D²Updated: July 2026
A 3/4-inch Type L copper line (C=130) over 80 feet with 50 psi available delivers roughly 12–15 GPM at acceptable velocity. Adequate for a shower plus one fixture simultaneously.
Tankless water heaters often require 8–10 GPM minimum. A 1-inch copper main over 40 feet at 60 psi provides ~20 GPM — sufficient headroom for a 199,000 BTU unit.
A 1/2-inch PEX branch (C=150) at 30 feet delivers ~4–5 GPM — enough for a lavatory but insufficient alone for a shower. Run 3/4-inch to the shower valve.
Hazen-Williams uses actual inner diameter. 3/4-inch Type L copper has an ID of 0.785 inches, not 0.75. Using nominal size overestimates flow capacity.
Static pressure at the meter is not available pressure at the fixture. Subtract friction loss over pipe length and fittings to get realistic flow at the point of use.
Plumbers and engineers need accurate flow rates to size pipes, select pumps, and verify fixture supply. This calculator estimates water flow in GPM from pipe diameter, available pressure, run length, and pipe material using the Hazen-Williams friction formula.