Darcy-Weisbach Head Loss Calculator
Use this Darcy-Weisbach calculator to find the head loss (or pressure drop) due to friction in a pipe, or reverse-solve for any other unknown: pipe diameter, flow velocity, friction factor, volumetric flow rate, or required pipe length. Enter your pipe geometry and fluid properties, choose a solve mode, and results appear instantly. The calculator auto-computes the Darcy friction factor from the Colebrook-White equation, classifies the flow regime, and shows power loss alongside every result.
Formula
Worked example
Water at 20 °C (ρ = 1000 kg/m³, ν = 1×10⁻⁶ m²/s) flows at 2 m/s through 100 m of 100 mm commercial steel pipe (ε = 0.046 mm). Re = 2 × 0.1 / 1e-6 = 200,000 (turbulent). ε/D = 0.046/100 = 0.00046. Colebrook-White gives f ≈ 0.0196. hf = 0.0196 × (100/0.1) × 4 / (2 × 9.807) ≈ 4.00 m. ΔP = 1000 × 9.807 × 4.00 ≈ 39,228 Pa. Q = 2 × π × 0.0025 ≈ 0.01571 m³/s. Power = 39,228 × 0.01571 ≈ 616 W.
What is the Darcy-Weisbach equation?
The Darcy-Weisbach equation calculates the head loss (energy lost per unit weight of fluid) due to friction as a fluid flows through a straight pipe. Written in its classic form it is hf = f (L/D) v² / (2g), where hf is head loss in metres (or feet), f is the dimensionless Darcy friction factor, L is pipe length, D is inner diameter, v is mean flow velocity, and g is gravitational acceleration. Multiplying head loss by fluid density and g gives the pressure drop: ΔP = ρ g hf. The equation applies to any Newtonian fluid (water, oil, air) in any flow regime, laminar or turbulent, making it the most widely used pipe friction formula in civil, mechanical, and chemical engineering.
How to find the friction factor: Colebrook-White and the Moody chart
The Darcy friction factor f is not a fixed property of the pipe - it depends on the Reynolds number (Re = vD/ν) and the relative pipe roughness (ε/D). In laminar flow (Re < 2300), the friction factor is exactly 64/Re, and roughness is irrelevant. In turbulent flow (Re > 4000), f is governed by the Colebrook-White equation: 1/√f = -2 log₁₀(ε/(3.7D) + 2.51/(Re √f)). Because f appears on both sides, it must be solved iteratively. This calculator uses 20 Newton-Raphson iterations seeded from the Swamee-Jain approximation, which converges to machine precision in practice. The Moody chart is simply a graphical representation of this equation across a range of Re and ε/D values. Between Re = 2300 and Re = 4000, flow is in the unstable transitional zone and results carry more uncertainty.
Six solve modes: any unknown from any four knowns
The standard Darcy-Weisbach equation has five variables (hf, f, L, D, v) plus the fluid properties (ρ, ν, ε). Given fluid properties and any four of the five main variables, you can solve for the fifth. This calculator offers six modes: (1) Head loss - the standard forward calculation; (2) Pipe length - how long a pipe can be for a given allowable head loss; (3) Pipe diameter - the minimum diameter needed to keep head loss within budget, solved iteratively because f depends on D; (4) Flow velocity - the velocity that produces a specified head loss in a known pipe, also iterative; (5) Friction factor - back-calculated from measured head loss and known geometry, useful for diagnosing fouled or corroded pipes; (6) Flow rate - the volumetric throughput corresponding to the solved velocity. All modes auto-compute Reynolds number, flow regime, and power loss.
Head loss vs pressure drop vs power loss
Head loss (hf, in metres or feet) expresses friction loss as an equivalent height of fluid column - it is independent of fluid density. Pressure drop (ΔP = ρ g hf, in Pascals or lbf/ft²) converts that height into force per unit area, so it depends on density. Power loss (P = ΔP × Q, in Watts or hp) is the rate at which mechanical energy is destroyed by friction - it is what a pump must supply to overcome the friction in that pipe section. These three quantities are all different ways of expressing the same physical loss; the right choice depends on the engineering context. Pump sizing uses head or pressure; energy cost calculations use power.
Typical absolute pipe roughness values (ε)
| Pipe material | Roughness ε (mm) | Condition |
|---|---|---|
| Drawn tubing (brass, copper, glass) | 0.0015 | Smooth |
| Wrought iron | 0.046 | New |
| Commercial steel | 0.046 | New |
| Galvanized iron | 0.15 | New |
| Asphalted cast iron | 0.12 | New |
| Cast iron | 0.26 | New |
| Concrete | 0.3 - 3.0 | Depends on finish |
| PVC / HDPE plastic | 0.0015 - 0.007 | Smooth |
| Stainless steel | 0.015 | New |
| Riveted steel | 0.9 - 9.0 | Rough |
Values from Moody (1944) and ASHRAE. Use these as starting points - actual roughness varies with age, corrosion, and deposits.
Frequently asked questions
What is the difference between Darcy-Weisbach and Hazen-Williams?
Both estimate pipe friction losses, but they work differently. Darcy-Weisbach is physically rigorous - it applies to any fluid, any flow regime, and any pipe material, using the friction factor from the Colebrook-White equation. Hazen-Williams is an empirical shortcut limited to water at ordinary temperatures and turbulent flow, expressed through a roughness coefficient C. Darcy-Weisbach is preferred for engineering design because of its generality; Hazen-Williams is still used in water distribution practice because its simpler form was easier to apply before computers.
What Reynolds number separates laminar from turbulent flow?
By convention, Re < 2300 is laminar (smooth, layered flow), Re > 4000 is turbulent (chaotic, mixing flow), and Re between 2300 and 4000 is the transitional zone. In practice, laminar flow can persist somewhat beyond 2300 in very smooth, undisturbed pipes, but any disturbance triggers turbulence. Most engineering pipe flows at normal velocities are turbulent (Re in the tens of thousands or higher), so the Colebrook-White equation is the typical path to the friction factor.
Why does doubling pipe diameter reduce head loss so dramatically?
Head loss scales as D^-5 when flow rate Q is held constant (not velocity). Substituting v = Q/(πD²/4) into the Darcy-Weisbach equation gives hf proportional to 1/D^5. Doubling the diameter at the same flow rate cuts head loss by a factor of 2^5 = 32, and power loss by the same factor. This is why upsizing a pipe by even one standard size can pay back its cost rapidly in energy savings for high-flow systems.
What pipe roughness value should I use for water pipes?
For new commercial steel or wrought iron pipes use ε = 0.046 mm. For drawn copper or brass tubing use ε = 0.0015 mm. For PVC or HDPE plastic use ε = 0.0015 to 0.007 mm. Cast iron is typically 0.26 mm. For older pipes, roughness grows with corrosion and deposits - aging cast iron can reach 1 mm or more. When in doubt for design purposes, use a conservative (higher) roughness value to avoid undersizing the pipe.
Can this calculator handle air or gas flow?
Yes, for incompressible or mildly compressible flow. Enter the gas density (air at 20 °C and atmospheric pressure is about 1.204 kg/m³) and kinematic viscosity (air ≈ 1.516e-5 m²/s at 20 °C). The Darcy-Weisbach equation applies directly as long as the pressure drop is small relative to the absolute pressure (roughly less than 10-15%). For high-pressure drops in gas systems, compressibility corrections are needed.
What does the power loss output mean in practice?
Power loss is the rate at which friction converts fluid mechanical energy into heat. In a pumped system, this is the minimum pump power needed just to overcome friction in that pipe section (before accounting for pump efficiency). If the calculated power loss is 2 kW, the pump motor must deliver at least 2 kW to the fluid for that pipe run, plus additional power for fittings, valves, static head, and pump inefficiency. Minimizing power loss by choosing a larger diameter or smoother pipe material directly cuts energy costs over the system lifetime.