Pressure Loss in Pipes

Friction with the pipe wall eats up pressure along the way. How much pressure does a pipe cost at a given flow, or how much can flow through it with the pressure you have? With the pipe material, length and bends taken into account.

FluidsPipesFriction

Inputs

Input examples

A straight round pipe full of fluid, steady flow. The friction factor f comes from 64/Re in laminar flow and the Colebrook equation in turbulent flow; between Re 2300 and 4000 the flow is unpredictable. ΣK adds the losses of bends, valves and fittings: add up the loss coefficient of each, from the manufacturer or a fluid-mechanics handbook.

Density ρ

Viscosity μ

Inner diameter D

Length L

Pipe material (roughness)

Roughness ε

Minor losses ΣK — bends, valves; 0 if none

Flow rate Q

Where the Pressure Goes

A fluid sticks to the pipe wall, so the layers in between rub against each other. That friction turns pressure into heat. The Darcy–Weisbach equation gives the loss: it grows with the length, falls steeply with the diameter, and grows with the square of the speed.

The friction factor f depends on the Reynolds number and on how rough the wall is compared with the diameter. In slow, laminar flow roughness does not matter; in fast, turbulent flow a rough old cast-iron pipe loses far more than a smooth plastic one. The Moody chart on the right shows the whole picture.

×2 flow≈ ×4 loss (turbulent)

×2 diameter≈ 1/32 of the loss

laminarf = 64 / Re

10 m head≈ 1 bar of water

Friction Factor (Moody Chart)

your pipe (ε/D)

perfectly smooth pipe

laminar: 64 / Re

your flow

Result

Enter the values above

Pipe Roughness

new pipes, typical values

Material	ε (mm)
Glass, plastic	0 (smooth)
Drawn tubing	0.0015
Commercial steel	0.045
Galvanized iron	0.15
Cast iron	0.26

Worked Techniques

Reynolds Number

First decide whether the flow is laminar or turbulent: that sets which friction law to use.

Example: water at 2.55 m/s in 50 mm: Re ≈ 127 000, turbulent.

Darcy–Weisbach

With f from Colebrook (solved by iteration, as the calculator does) or read from the Moody chart.

Example: 100 m of 50 mm steel at 5 L/s: about 1.4 bar.

Head Loss

The same loss as a height of fluid column: the extra height a pump has to deliver to overcome the friction.

Example: 1.4 bar of water ≈ 14 m of head.

Sources & Verification

References

Y. A. Çengel & J. M. Cimbala, Fluid Mechanics: Fundamentals and Applications, 4th ed., McGraw-Hill, 2018 — Ch. 8 (Internal Flow).
F. M. White, Fluid Mechanics, 8th ed., McGraw-Hill, 2016 — Ch. 6 (Viscous Flow in Ducts).