Compute the frictional pressure drop and head loss in a straight pipe with the Darcy-Weisbach equation. The calculator finds the Reynolds number and the Darcy friction factor for you — using 64/Re in laminar flow and the Swamee-Jain explicit correlation in turbulent flow.
Every pump, compressor, and gravity-fed line must overcome the friction between a moving fluid and the pipe wall. The Darcy-Weisbach equation is the rigorous, dimensionally consistent way to predict that frictional pressure drop, and it works for any fluid in any unit-consistent system. This calculator pairs it with automatic Reynolds-number and friction-factor evaluation so you only enter physical quantities.
ΔP = f · (L/D) · (ρ·v²/2), and the equivalent head loss h_f = f · (L/D) · (v²/2g).
Here f is the Darcy friction factor (dimensionless), L the pipe length, D the inside diameter, ρ the density, v the average velocity, and g = 9.81 m/s². The group ρv²/2 is the dynamic pressure, and L/D scales it by how long and how narrow the pipe is. Note the Darcy friction factor is four times the Fanning friction factor — using the wrong one is a classic factor-of-four error.
In laminar flow (Re < 2300) the friction factor is exact: f = 64/Re. In turbulent flow it depends on both Re and the relative roughness ε/D and is read from the Moody chart or computed from the implicit Colebrook equation. This tool uses the explicit Swamee-Jain approximation, f = 0.25 / [log₁₀(ε/3.7D + 5.74/Re^0.9)]², which matches Colebrook within about 1% over the normal turbulent range — accurate enough for design without iteration.
The absolute roughness ε depends on the pipe material. Typical values (m): drawn tubing/glass 0.0000015, commercial steel 0.000045, galvanized iron 0.00015, cast iron 0.00026, concrete 0.0003–0.003. As a pipe ages and scales, ε grows, so designers often add margin. For smooth plastic pipe ε is essentially zero and the flow approaches the hydraulically smooth limit.
This calculator gives the straight-pipe (major) loss. Real systems also have minor losses from valves, bends, expansions, and fittings, usually written h_minor = K·v²/2g with a loss coefficient K, or as an equivalent length added to L. Sum the major loss, all minor losses, and any static elevation change to get the total dynamic head the pump must deliver — then read the required head off the pump curve.
They describe the same physics but differ by a factor of four: f_Darcy = 4 · f_Fanning. The Darcy-Weisbach equation uses the Darcy factor (laminar value 64/Re); chemical engineering texts that use the Fanning factor have a laminar value of 16/Re. This calculator uses the Darcy convention. Always confirm which one a chart or correlation reports.
The Swamee-Jain explicit correlation agrees with the implicit Colebrook equation to within about 1% for Reynolds numbers from 5,000 to 10⁸ and relative roughness up to 0.05 — well within engineering accuracy and avoiding the need for iteration. For laminar flow the calculator switches to the exact f = 64/Re.
No — it computes the straight-pipe (major) frictional loss only. To get total system pressure drop, add minor losses from valves, elbows, tees, and reducers using K·v²/2g or the equivalent-length method, plus any change in elevation (static head). Those combined give the total dynamic head for pump selection.
Because pressure drop scales roughly with 1/D⁵ at fixed flow rate: halving the diameter raises velocity four-fold (v ∝ 1/D²) and the loss term carries v²/D, so the drop climbs dramatically. This is why slightly oversizing a line is one of the cheapest ways to cut pumping energy over a plant's life.
For low pressure drops (under ~10% of the absolute pressure) where density is roughly constant, yes — treat the gas as incompressible and use its density and viscosity at operating conditions. For large pressure drops or high velocities, compressibility matters and you need a compressible-flow method (isothermal or adiabatic pipe-flow equations) instead.