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Darcy-Weisbach Head Loss Calculator

Reference: Darcy-Weisbach / Moody
🌊 MECH
Free Darcy-Weisbach head loss calculator. Find pipe friction head loss (ft), pressure drop (psi) and velocity from flow, diameter, length and friction factor. US units, worked examples.
Inputs
Enter the flow rate, pipe inside diameter, length and Darcy friction factor. The calculator returns the head loss, pressure drop, velocity and friction per 100 ft.
Results
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ℹ About This Calculator

The Darcy-Weisbach equation is the most general and accurate way to calculate friction head loss in a pipe, valid for any fluid and any flow regime. This calculator computes the friction head loss (in feet and psi) and the flow velocity from the flow rate, pipe diameter, length and Darcy friction factor, in US units. It is the core of hydraulic design — sizing pumps, checking pressure availability, and verifying velocity — and is preferred over Hazen-Williams for non-water fluids and precise work because it is dimensionally consistent and physically based.

The Darcy-Weisbach equation relates head loss to the friction factor, the length-to-diameter ratio, and the velocity head. The friction factor f depends on the Reynolds number and the pipe's relative roughness, read from the Moody chart or computed with the Colebrook equation; typical values for turbulent flow in commercial pipe are 0.015 to 0.03. Unlike the empirical Hazen-Williams formula (limited to water), Darcy-Weisbach works for any fluid and is dimensionally correct, making it the method of choice for gases, oils and precise engineering.

Darcy-Weisbach Equation

Darcy-Weisbach / Moody

h_f = f · (L/D) · (V²/2g), where f = Darcy friction factor, L = length, D = inside diameter (ft), V = velocity (ft/s), g = 32.2 ft/s². Velocity V = 0.408·Q/d² for water (Q in GPM, d in inches). Pressure drop (psi) = h_f × 0.4335.

Worked Example

Water flows at 100 GPM through 100 ft of 2-inch pipe with a friction factor of 0.02. Velocity V = 0.408 × 100 / 2² = 10.2 ft/s. Head loss h_f = 0.02 × (100/0.167) × (10.2²/64.4) = 19.4 ft, or about 8.4 psi.

Frequently Asked Questions

What is the Darcy-Weisbach equation? +
The Darcy-Weisbach equation calculates friction head loss in a pipe as h_f = f·(L/D)·(V²/2g), where f is the Darcy friction factor, L the length, D the inside diameter, V the velocity, and g gravity. It is the most general head-loss equation because it is dimensionally consistent and works for any fluid and flow regime, unlike the empirical Hazen-Williams formula which is limited to water at ordinary temperatures.
What is the difference between Darcy-Weisbach and Hazen-Williams? +
Both calculate pipe friction loss, but Darcy-Weisbach is physically based and dimensionally consistent, valid for any fluid (water, oil, gas) and any temperature, using a friction factor from the Moody chart. Hazen-Williams is a simpler empirical formula calibrated only for water at typical temperatures, using a roughness coefficient C. Engineers use Hazen-Williams for convenience in water systems and Darcy-Weisbach when accuracy or non-water fluids matter.
How do I find the friction factor? +
The Darcy friction factor depends on the Reynolds number and the pipe's relative roughness (roughness divided by diameter). For laminar flow it is simply 64/Re; for turbulent flow it is read from the Moody chart or computed with the Colebrook equation. For commercial steel or plastic pipe in turbulent flow, it typically ranges from about 0.015 to 0.03, decreasing as the pipe gets larger and smoother.
How do I convert head loss to pressure drop? +
For water, multiply the head loss in feet by 0.4335 to get pressure drop in psi (since 1 psi = 2.31 ft of water). So a head loss of 19.4 ft equals about 8.4 psi. The conversion depends on fluid density, so for fluids other than water use the fluid's specific gravity: pressure drop (psi) = head loss (ft) × 0.4335 × specific gravity.
Why does velocity matter so much in head loss? +
Because head loss is proportional to the square of velocity (V²) in the Darcy-Weisbach equation, so doubling the velocity quadruples the friction loss. This is why oversizing velocity to save pipe cost backfires with steeply rising pump energy, and why keeping pipe velocity in the 4-8 ft/s range balances pipe cost against friction. High velocity also causes noise and erosion.
Does the Darcy-Weisbach equation work for air and gases? +
Yes — that is one of its main advantages over Hazen-Williams. Because it is dimensionally consistent, Darcy-Weisbach applies to any Newtonian fluid, including air, natural gas and oils, using the appropriate density and viscosity to find the Reynolds number and friction factor. For compressible gases at high pressure drops, additional compressibility corrections are applied, but for low-pressure-drop cases the basic equation works well.
Is this head loss calculator accurate? +
It applies the exact Darcy-Weisbach equation, so it is accurate provided you use the correct friction factor for your Reynolds number and pipe roughness. The main source of error is the friction factor itself, so for precise work determine f from the Moody chart or Colebrook equation at your actual flow conditions. For fittings, add their equivalent length or loss coefficients to the pipe friction.

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