Pipe Flow Calculator
Work out the velocity, friction factor, head loss and pressure drop for water moving through a pipe.
What it does
Water moving through a pipe rubs against the walls, and that rubbing costs energy. The height the water loses over a length of pipe is the head loss, and the same number turned into pressure is what a pump has to make up. The standard way to work it out is the Darcy-Weisbach equation, which the Natural Resources Conservation Service prints in its pipe flow chapter and the Bureau of Reclamation uses in its water measurement manual.
The equation has three moving parts. The friction factor describes how rough the pipe is, the ratio of length to diameter says how much pipe the water has to rub against, and the velocity squared says how hard it is rubbing. That last part is why a small pipe is so punishing: halving the diameter of a pipe at the same flow rate quadruples the velocity and multiplies the head loss by sixteen.
The friction factor itself is not a constant. For turbulent flow it comes from the Colebrook-White equation, which links the roughness of the pipe to the Reynolds number, and it has to be solved by iteration because the friction factor appears on both sides. The roughness values used here are the ones in the NRCS table, from 0.046 millimetres for commercial steel down to 0.0015 for drawn copper.
Water temperature matters because warm water is thinner. The density and viscosity used come from the NIST reference data for water at atmospheric pressure, and they are what sets the Reynolds number, which decides whether the flow is laminar or turbulent.
What this page does not include is the rest of the system. Fittings, elbows, tees and valves add their own losses, and so do the entrance and the exit. A garden line with a dozen fittings will lose more than the straight pipe suggests, and any real design has to add a fitting allowance on top.
How to use
- Pick imperial or metric units.
- Choose the pipe material, since the roughness drives the friction factor.
- Enter the inside diameter of the pipe, not the outside.
- Enter the length of the run.
- Enter the flow rate and the water temperature.
- Read the velocity first, because a pipe running too fast is the most common design mistake.
Formula
- h_f
- Head lost along the pipe, in metres of water.
- f
- Darcy friction factor, dimensionless.
- L, D
- Length and inside diameter of the pipe.
- V
- Mean velocity of the flow.
- Re
- Reynolds number, which uses the kinematic viscosity nu of the water.
This is the Darcy friction factor, not the Fanning factor, so the head loss equation has no extra factor of four in front of it. The equation is valid for a full circular pipe running full, and it describes straight pipe friction only. Where the flow is laminar, below a Reynolds number of about 2300, the friction factor is simply 64 divided by the Reynolds number and roughness stops mattering.
Worked example
Example: 100 mm steel pipe, 100 m long, 20 L/s at 20 °C
Defaults: metric units, commercial steel, 100 mm inside diameter, 100 m of pipe, 20 liters per second and water at 20 °C.
- Area: pi x 0.1 squared / 4 = 0.007854 m2, so the velocity is 0.020 / 0.007854 = 2.55 m/s.
- Water at 20 °C has a kinematic viscosity of 1.0034e-6 m2/s, so the Reynolds number is 2.5465 x 0.1 / 1.0034e-6 = 253,785.
- With a roughness of 0.046 mm, the Colebrook-White equation converges on a friction factor of 0.0182.
- Head loss: 0.0182 x (100 / 0.1) x (2.5465 squared / 2 x 9.80665) = 6.02 m.
- Pressure drop: 998.2 kg/m3 x 9.80665 x 6.02 m = 58,968 Pa, which is 0.590 bar or 8.55 psi.
- The tool shows 2.55 m/s, 253,785, 0.0182, 6.02 m and 0.590 bar.
Reference table
| Pipe and material | Velocity | Friction factor | Head loss per metre |
|---|---|---|---|
| 100 mm steel, 100 m | 2.55 m/s | 0.0182 | 0.060 m per m |
| 50 mm PVC, 50 m | 5.09 m/s | 0.0153 | 0.405 m per m |
| 25 mm copper, 100 m | 10.19 m/s | 0.0155 | 3.275 m per m |
Limits
- Covers straight pipe friction, with no allowance for fittings, valves, entrances or exits.
- Assumes the pipe runs full and the flow is steady.
- Uses one roughness value per material, while real pipes vary with age, scaling and deposits.
- Says nothing about the pump curve, so the result is a requirement rather than a selection.
Common mistakes
- Using the outside diameter instead of the inside diameter, which understates the loss.
- Forgetting that the velocity term is squared, so a small diameter change moves the answer a long way.
- Using the Fanning friction factor with the Darcy head loss equation, which gives a result four times too small.
- Ignoring the fittings, which often add more loss than the straight pipe in a short run.
- Leaving the water temperature out, even though cold water is slower moving and adds a little loss.
Try it yourself
Quick checks. Answers sit tucked under each question.
How much head does 100 m of 100 mm steel lose at 20 L/s?
6.02 m of head, which is 0.590 bar or 8.55 psi of pressure drop.
What happens if the same flow goes through 25 mm copper instead?
The velocity rises to 10.19 m/s and the head loss over 100 m becomes 327.50 m, which is 32.059 bar. The same water through a pipe a quarter the diameter is punishing.
What is the head loss per metre in 50 mm PVC carrying 10 L/s?
The velocity is 5.09 m/s with a friction factor of 0.0153, so the loss is 20.24 m over 50 m, which is 0.405 m per metre.
Questions
What is head loss?
The height the water drops because of friction in the pipe. One metre of head is the pressure of a column of water one metre high, which is about 9.81 kPa or 0.098 bar.
Why does pipe diameter matter so much?
Because the velocity goes as the inverse square of the diameter at a given flow, and the head loss goes as the velocity squared. A pipe a quarter the diameter loses sixteen times as much head per metre.
What is the Colebrook-White equation?
It is the standard way of finding the friction factor in a turbulent pipe, combining the roughness of the pipe and the Reynolds number. It has to be solved by iteration because the friction factor appears inside the logarithm.
What is a good velocity for a pipe?
For irrigation and general water service, staying under about 2 metres per second keeps the noise and the erosion down. The calculator makes it easy to see which pipe size keeps a given flow under that.
Does the pipe material change the answer much?
Less than the diameter does. Steel, PVC and copper have roughness values within a few hundredths of a millimetre of each other, while the size of the pipe and the flow rate dominate the result.
What about fittings and bends?
Each elbow, tee and valve has its own equivalent length, and the manuals list them. Those losses are added to the straight pipe figure that this page gives.
Sources
- USDA Natural Resources Conservation Service: National Engineering Handbook, Chapter 4, pipe flow
- US Bureau of Reclamation: Water Measurement Manual, chapter 2, pipe flow
- NIST Chemistry WebBook: density and viscosity of water at atmospheric pressure