Science & Engineering
Pressure drop in a pipe.
Friction pressure loss and head loss for water or another fluid in a full, straight circular pipe, from the Darcy-Weisbach equation with a Swamee-Jain friction factor. Runs in your browser.
Flow, pipe and fluid
Result
Fill the form and press Calculate.
Worked example
Water at 20 °C (998.21 kg/m³, 1.0016 mPa·s) flows at 2 L/s through 100 m of 50 mm commercial steel pipe, roughness 0.09 mm. Velocity = 0.002 ÷ (π × 0.05² ÷ 4) = 1.02 m/s and Re = 998.21 × 1.0186 × 0.05 ÷ 0.0010016 = 50,757, so the flow is turbulent. Relative roughness is 0.09 ÷ 50 = 0.0018, and the Swamee-Jain friction factor is f = 0.0263. Pressure drop = f × (L ÷ D) × ρ v² ÷ 2 = 0.0263 × 2,000 × 517.8 = 27.2 kPa (3.94 psi), a head loss of 2.78 m of water.
How it works
The Darcy-Weisbach equation gives the friction pressure loss along a full pipe as Δp = f × (L ÷ D) × ρ v² ÷ 2, where f is the Darcy friction factor, L the length, D the inside diameter, ρ the density and v the mean velocity. Head loss is Δp ÷ (ρ g). For laminar flow (Reynolds number below 2,000) f = 64 ÷ Re. For turbulent flow the page uses the Swamee-Jain approximation of the Colebrook equation, f = 0.25 ÷ [log₁₀(ε ÷ 3.7D + 5.74 ÷ Re^0.9)]², published for 5,000 ≤ Re ≤ 10⁸ and 0.000001 ≤ ε ÷ D ≤ 0.05. Between Re 2,000 and 4,000 the flow is unsteady and poorly understood, so the larger of the laminar and turbulent factors is shown with a warning, and values outside the fit's range are flagged.
Water density and viscosity come from tabulated values at 10 to 60 °C. Roughness is the upper end of the range listed for each material, to avoid understating the loss; new or smooth pipe will usually lose less and old, corroded pipe more. The calculator assumes steady flow of an incompressible fluid in a full, round pipe.
Not for system design
Planning and learning aid only. It is not for structural, pressure-system or other safety-critical design, and it is not professional engineering advice. Have a qualified engineer check anything that carries people or could fail dangerously. Size pumps, pressure ratings and relief devices from a full analysis, not from this estimate.
Sources and basis: Darcy-Weisbach equation (Wikipedia); Darcy friction factor formulae (Wikipedia); Surface Roughness Coefficients (Engineering ToolBox); Water - Dynamic and Kinematic Viscosity at Various Temperatures and Pressures (Engineering ToolBox); Water Density, Specific Weight and Thermal Expansion Coefficients (Engineering ToolBox). Checked 2026-10-08. Planning aid only; see the note above.
FAQ
What is the Darcy-Weisbach equation?
Δp = f × (L ÷ D) × ρ v² ÷ 2: friction pressure loss grows with pipe length and with the square of velocity, and shrinks with a larger diameter. f is the dimensionless Darcy friction factor.
How is the friction factor found?
For laminar flow f = 64 ÷ Re. For turbulent flow this page uses the Swamee-Jain equation, an explicit approximation of the Colebrook equation, using the pipe's relative roughness and the Reynolds number.
Why use the upper end of the roughness range?
To avoid understating friction. New or smooth pipe usually has a lower roughness and a lower loss; corroded or scaled pipe has more.
Does it include fittings and valves?
No. It covers straight pipe only. Add losses for fittings, valves and entrances separately, and account for any elevation change.
Why is there a warning at Reynolds 2,000 to 4,000?
In that critical range the flow is unsteady and varies along the pipe, so no formula is reliable. The calculator shows the larger of the laminar and turbulent friction factors.