How to use this calculator

Enter the flow rate, the pipe’s inside diameter and length, and pick the pipe material and fluid. To include elbows, valves and entrances, add their loss coefficients into ΣK. The chart shows how the pressure drop climbs with flow, roughly with the square of the flow rate in turbulent flow.

Formulas

Velocity and Reynolds numberV = QπD²/4 Re = ρ V Dμ

Darcy–Weisbach head loss and pressure droph_L = f LD V²2g + ΣK V²2g Δp = ρ g h_L

Friction factor: laminar (Re < 2,300)f = 64Re

Friction factor: turbulent, Colebrook equation (solved iteratively)1√f = −2 log₁₀(ε/D3.7 + 2.51Re √f)

The Colebrook equation is the formula behind the Moody chart. The calculator solves it exactly instead of using an approximation such as Swamee–Jain.

Worked example

5 L/s of 20 °C water in 100 m of 2 in Schedule 40 steel pipe (the default)

D = 52.5 mm, so A = 2.165 × 10⁻³ m² and V = 0.005 / 0.002165 = 2.31 m/s.
Re = 998.2 × 2.31 × 0.0525 / 0.001002 = 120,800: turbulent.
ε/D = 0.045 / 52.5 = 0.000857, and Colebrook gives f = 0.0213.
h_L = 0.0213 × (100 / 0.0525) × 2.31² / (2 × 9.807) = 11.0 m, so Δp = 998.2 × 9.807 × 11.0 = 108 kPa (15.7 psi).

Typical fitting loss coefficients

Fitting	K (approximate)
Standard 90° elbow, threaded	0.75–1.5
Long-radius 90° elbow, flanged	0.2–0.4
Gate valve, fully open	0.15
Globe valve, fully open	10
Sharp-edged pipe entrance	0.5
Pipe exit into a tank	1.0

Assumptions and limits

Steady, incompressible, fully developed flow in a full, circular pipe.
For gases, results are reasonable when the pressure drop is less than about 10% of the inlet pressure; beyond that, density changes along the pipe.
Elevation change is not included. Add ρgΔz to get the total pressure difference between two points at different heights.
Roughness values are for new pipe. Old, corroded or scaled pipe can be much rougher.

Frequently asked questions

Darcy or Fanning friction factor?

This calculator uses the Darcy factor, the one on the Moody chart. The Fanning factor used in some chemical engineering texts is one quarter of it.

What about the Hazen–Williams formula?

Hazen–Williams is an empirical formula for water only at ordinary temperatures. Darcy–Weisbach works for any Newtonian fluid and is more accurate, especially for small pipes and high velocities.

How do I find the pump head I need?

Add the head loss from this calculator to the elevation the fluid must rise and any pressure difference between the source and destination, expressed as head.

For education and preliminary checks only. Have a qualified engineer verify any design before it is built.