Pipe flow calculator

What the calculator returns

Give it a pipe, a fluid and a flow, and it returns ten quantities. The flow can be a mean velocity or a volumetric rate, and the roughness can be typed or filled from a named material. Every result has a copy button.

• Mean velocity, V, and volumetric flow, Q: whichever you did not give, from the bore area
• Reynolds number, Re = ρVD/μ: dimensionless, the ratio of inertial to viscous forces
• Flow regime: laminar below Re 2300, transitional to 4000, turbulent above
• Relative roughness, ε/D: dimensionless, and the second axis of the Moody chart
• Darcy friction factor, f: 64/Re when laminar, Colebrook-White when turbulent
• Pressure drop, Δp: in Pa and in bar, from Darcy-Weisbach over the length you give
• Head loss, h_f: in metres of the flowing fluid, which is Δp/ρg
• Wall shear stress, τ_w = fρV²/8: in Pa, which sizes erosion and fouling arguments

Correlations, and how they were checked

Laminar flow uses f = 64/Re, which is exact, being the Hagen-Poiseuille solution rather than a fit. Turbulent flow uses the Colebrook-White equation, which is implicit in f and is solved here by iteration from the Swamee-Jain explicit form. Pressure drop is Darcy-Weisbach.

The friction factor was checked before this page existed, and checked twice, because two implementations of mine agreeing would only show that I had not made two different mistakes. It was solved independently by a root finder rather than by iteration, agreeing to twelve decimal places, and then compared against published Moody values:

Where it refuses to answer, and why

A calculator that always returns a number is not more useful than one that says when it cannot. This one declines in three places.

• Between Re 2300 and 4000 it answers and warns. No friction correlation is reliable through the transition. The turbulent value is shown so there is something to work with, labelled transitional, rather than printed with the confidence of a number at Re 10⁵
• Above ε/D of 0.05 it refuses. That is outside the range Colebrook covers, and the usual cause is a roughness or a diameter entered in the wrong unit
• An unconverged solve returns nothing. A friction factor that quietly stopped iterating early is worse than no friction factor, and a refusal also clears the panel so a previous answer cannot sit there looking current

A worked case you can reproduce

Water at 20 °C through 100 m of 100 mm commercial steel pipe at 2 m/s. Density 998.2 kg/m³, dynamic viscosity 0.001002 Pa·s, roughness 0.045 mm.

• Reynolds number: 199,242, so turbulent
• Relative roughness: 0.00045
• Friction factor: 0.01857
• Pressure drop: 37,067 Pa, which is 0.371 bar
• Head loss: 3.787 m of water
• Wall shear stress: 9.267 Pa

For dry air, take the density and viscosity from the air properties calculator first: it returns both from a temperature, and density needs a pressure as well.