How to use the darcy-weisbach pipe friction calculator
- Enter the flow rate in liters per second, the inside diameter in millimeters and the pipe length in meters.
- Enter the wall roughness in millimeters. The page starts with 0.046 as an example for new steel pipe, so use the value for your own pipe.
- Choose the fluid: water at 20 C or 60 C, air at 20 C, or your own, in which case enter the kinematic viscosity and density.
- Read the head loss, the pressure drop, the flow speed, the Reynolds number, the flow regime and the friction factor, with a check against a second formula.
Formula
Head loss h = f x (L / D) x v^2 / (2 g), and pressure drop = density x g x h
Reynolds number Re = v x D / kinematic viscosity, with v = flow / (pi x D^2 / 4)
Laminar flow (Re under 2,300): f = 64 / Re
Turbulent flow: 1 / sqrt(f) = -2 log10(roughness / (3.7 D) + 2.51 / (Re x sqrt(f))), solved by iteration (Colebrook)
The Swamee-Jain formula is an explicit approximation of the Colebrook equation, and the page shows it as a check. The two should agree within about one to two percent for ordinary turbulent flow.
10 liters per second in 100 m of 50 mm steel pipe
The area of a 50 mm pipe is 0.0019635 square meters, so 10 liters per second gives a speed of 5.093 m/s. With the kinematic viscosity of water at 20 C the Reynolds number is 253682, so the flow is turbulent. The Colebrook friction factor is 0.020434.
The head loss over 100 m is 0.020434 x (100 / 0.05) x 5.093^2 / (2 x 9.80665) = 54.048 m, which is a pressure drop of 529.08 kPa. The Swamee-Jain value of 0.020582 is 0.72 percent apart from the Colebrook result. A loss this large tells you the pipe is too small for that flow.
When to use Darcy-Weisbach
The Darcy-Weisbach equation applies to any Newtonian fluid, any pipe size and any flow regime, so it works for oil, air and hot water as well as cold water. The Hazen-Williams method is simpler but is limited to water at ordinary temperatures in turbulent flow. When both apply, compare the answers with the Hazen-Williams pipe pressure drop calculator.
To convert a flow rate and a pipe size to a speed on its own, use the flow rate calculator. To find the volume of fluid the pipe holds, use the pipe volume calculator.
The transition zone
Between a Reynolds number of about 2,300 and 4,000 the flow is unstable and may switch between laminar and turbulent. The page labels this range as transitional and uses the turbulent equation, which gives a safe, higher loss. Do not expect a precise answer there.
Fittings, valves and bends add losses that this page does not include. Add them separately as a number of velocity heads, or as an equivalent length of straight pipe.
Assumptions and limits
- The pipe is full, round, straight and level, and the flow is steady.
- Roughness, viscosity and density are examples or values you supply. Use data for your own pipe and fluid.
- Minor losses from fittings are not included.
- Gravity is taken as 9.80665 m/s2, and the fluid is treated as incompressible, which is reasonable for air only at low pressure drops.
Frequently asked questions
What is the Darcy friction factor?
It is a dimensionless number that tells how much energy a pipe wall takes from the flow. It depends on the Reynolds number and on the roughness compared with the diameter.
How is this different from Hazen-Williams?
Darcy-Weisbach comes from fluid mechanics and works for any fluid. Hazen-Williams is an empirical formula for water, and it is simpler but less general.
What roughness should I use?
Use the value from the pipe maker or a reference for the material. The 0.046 mm figure on the page is an example for new commercial steel. Old or corroded pipe can be much rougher.
Why does the page show two friction factors?
The main value solves the Colebrook equation by iteration. The second is the Swamee-Jain approximation, shown as a check on the result.