How much pressure is lost in the pipe?

How do I calculate friction loss in a pipe?

With the Hazen-Williams formula used in NFPA 13: loss in psi per foot = 4.52 × Q^1.85 ÷ (C^1.85 × d^4.87), where Q is the flow in GPM, d the inside diameter in inches and C the pipe's roughness factor. 10 GPM through 100 feet of 1 inch type L copper loses about 2.67 psi.

What is the Hazen-Williams C factor?

A number for how smooth the inside of the pipe is — higher is smoother. NFPA 13 uses 150 for copper and plastic pipe such as PVC, CPVC and PEX, and 120 for galvanized steel. Old, scaled pipe can be much lower.

How do I convert psi to feet of head?

Multiply by 2.307: a pound per square inch holds up a column of water 2.307 feet tall. A 2.67 psi loss is 6.2 feet of head — the number pump curves use.

Do fittings add friction loss?

Yes. Elbows, tees and valves each add loss, usually counted as an equivalent length of straight pipe from the fitting maker's or NFPA 13's tables. Add those feet to the pipe length for a closer answer.

Why does loss rise so fast with flow?

Because the flow is raised to the power 1.85: doubling the flow multiplies the loss by about 3.6. A larger pipe helps even more — going up one size often cuts the loss by more than half.

Worked example: 10 GPM through 100 feet of copper

Take 10 GPM through 100 feet of 1 inch type L copper, whose inside diameter is 1.025 inches, with C = 150. The formula gives 0.0267 psi per foot, so 2.67 psi over the run, which is 6.2 feet of head. The water moves at 3.9 feet per second. Changing to 1¼ inch type L (inside diameter 1.265 inches) drops the loss to 0.96 psi and the speed to 2.6 feet per second. Doubling the flow in the 1 inch pipe to 20 GPM raises the loss to 9.64 psi, 3.61 times as much. The same 1 inch size in galvanized steel (C = 120) would lose 4.04 psi.

What does the formula assume, and where does it stop being valid?

Hazen-Williams is an empirical formula for water, not a derivation from fluid mechanics, so it has no term for temperature or viscosity: it is meant for water at ordinary temperatures flowing in full, turbulent pipes. For oils, glycol mixtures or steam, use the Darcy-Weisbach equation instead. The C factor is also an assumption about the pipe's condition: table values describe pipe in good shape, and an old, scaled steel line can be rougher than the C = 120 used here for galvanized steel.

Does a change in height add to the friction loss?

No, it adds separately. Friction loss is the pressure used up by moving water along the pipe. Lifting water also costs pressure, but that is static head: with 1 psi equal to 2.307 feet of water, every foot of rise takes about 0.433 psi, and a drop gives the same amount back. For a pump, add the friction head to the vertical lift to get the total head it must overcome.

Common mistakes with friction loss

Using the nominal pipe size as the inside diameter: a 1 inch type L copper tube is 1.025 inches inside, and PEX, PVC and galvanized pipe of the same nominal size have other inside diameters, which matters because the diameter is raised to the power 4.87. Entering liters per minute as GPM, which overstates the flow by almost four times (the metric mode of the calculator converts for you). Forgetting fittings, valves and meters, which can add more loss than a short straight run. Reading the answer as the pressure at the fixture: the loss is subtracted from the pressure available at the start of the run.

Sources and related calculators

Sources: NFPA 13, Standard for the Installation of Sprinkler Systems, Table 28.2.4.8.1 (Hazen-Williams C values) and the Hazen-Williams formula in its NFPA form; ASME B36.10 for Schedule 40 inside diameters. Related: pipe velocity calculator, pipe size calculator, head pressure calculator and pressure calculator.