Pipe flow and pressure drop calculator

This free pipe pressure drop calculator works out the head loss and pressure drop of a liquid flowing in a circular pipe using the Darcy-Weisbach equation, or turns the question around and finds the flow that a given available head will drive. It has built-in fluid presets, a standard pipe-size picker (Sch 10, 40, 80 and 160, ASME B36.10M), a pipe-material roughness dropdown, and a metric or imperial toggle. It uses the same physically based method as Fluid Network Studio, so it is valid across the laminar, transitional and fully turbulent ranges rather than being tied to one fluid or one roughness.

Method

Head loss along a straight, full, circular pipe is given by the Darcy-Weisbach equation:

h_f = f (L / D) (v^2 / 2g)

and the pressure drop is dp = rho g h_f, where h_f is head loss (m), f is the Darcy friction factor, L is length (m), D is internal diameter (m), v is mean velocity (m/s), g is standard gravity (9.80665 m/s^2, the value the calculator and the Studio both use) and rho is density (kg/m^3).

Mean velocity comes from continuity, v = Q / A with A = pi D^2 / 4, and the flow regime is set by the Reynolds number Re = rho v D / mu = v D / nu.

The friction factor depends on the regime:

• Laminar: f = 64 / Re (the calculator applies this exact law up to Re = 2000).
• Turbulent: the Colebrook-White equation,

1 / sqrt(f) = -2 log10( (epsilon/D) / 3.7 + 2.51 / (Re sqrt(f)) )

which is implicit in f and whose graphical form is the Moody chart. Fluid Network Studio and this calculator evaluate it with the explicit Churchill (1977) correlation across all flow regimes. To read the friction factor on its own, use the Darcy friction factor calculator.

Colebrook (1939) and Moody (1944) are the classical sources for the turbulent friction factor, and Churchill (1977) is the explicit correlation actually evaluated here. All three are listed with links in the references at the foot of this page.

Assumptions and limits. Steady, incompressible, single-phase Newtonian flow in a full circular pipe of uniform diameter. Fittings and minor losses are not included here (build the line in the Studio to add them). For compressible gas, non-Newtonian fluids or a network of pipes, use the Studio.

Inputs

• Fluid preset (sets density and viscosity) or a custom density (kg/m^3) and kinematic viscosity (m^2/s).
• Internal diameter D, typed or filled from the standard pipe-size picker.
• Length L.
• Absolute roughness, from the pipe-material dropdown or entered directly.
• Mode A: flow Q, to find head loss and pressure drop.
• Mode B: available head, to find the flow.

Outputs

• Mean velocity and Reynolds number, with the flow regime.
• Darcy friction factor.
• Head loss and pressure drop (in SI, both kPa and bar).
• In Mode B, the resulting flow.

Absolute roughness of common pipe materials

These are the same values behind the calculator's material dropdown, indicative figures from the Moody chart and Crane TP-410. Old, corroded or fouled pipe is rougher, so verify the condition for design work.

Typical design velocities for liquid lines

Check the velocity row in the result against these bands. See the pipe velocity calculator to size a pipe to a target velocity.

Reasonable-practice ranges of the kind published in Crane TP-410 and pump handbooks. Keep suction lines to the low end to protect NPSH, and expect noise and erosion risk much above 3 m/s in building services.

Water density and kinematic viscosity by temperature

Standard saturated liquid-water properties (see White, Fluid Mechanics, or Incropera and DeWitt). Presets for water at 10, 20 and 40 degrees C are built in, so pick Custom and enter these values for other temperatures.

Worked example

Water at 20 degrees C (density 998.2 kg/m^3, kinematic viscosity 1.0036 x 10^-6 m^2/s, both taken from the built-in water correlation) in a 100 mm commercial-steel pipe (roughness 0.045 mm), 50 m long, carrying 20 L/s.

1. Area A = pi (0.1)^2 / 4 = 0.007854 m^2, so v = 0.020 / 0.007854 = 2.546 m/s.
2. Re = v D / nu, which comes to 253,746 on the unrounded velocity (turbulent).
3. Relative roughness epsilon/D = 0.045/100 = 4.5 x 10^-4, and the Churchill friction factor is f = 0.01827.
4. h_f = 0.01827 x (50/0.1) x (2.546^2 / (2 x 9.80665)) = 3.02 m.
5. dp = 998.2 x 9.80665 x 3.02 = 29.6 kPa.

Those are the figures the calculator above returns for the same inputs, because this worked example is run on the same Churchill correlation the widget and the Studio evaluate, not on a different friction model.

Churchill against Colebrook-White. Solving the implicit Colebrook-White equation at the same Reynolds number and relative roughness gives f = 0.01816, so h_f = 3.00 m and dp = 29.4 kPa. That is 0.6 per cent below the Churchill value, which is the known accuracy of the explicit correlation against the implicit one and is far smaller than the uncertainty in the absolute roughness you enter. If you are checking this page against a textbook worked on Colebrook-White, expect a difference of that order and no more.

Reverse (Mode B): a 150 mm steel pipe, 200 m long, with 10 m of available head drives about 52.8 L/s (velocity 2.99 m/s, Re about 446,000, f = 0.0165). Turn the required head into pump power with the pump power calculator.

Frequently asked questions

How do I find the flow from a known pressure drop?

Switch the calculator to its Available head to flow mode and enter the driving head. For water, 1 bar of pressure drop is about 10.2 m of head. The calculator then inverts the Darcy-Weisbach relation numerically on the same physics as the forward mode.

Does it work in imperial units (gpm and psi)?

Yes. The Metric (SI) and Imperial (US) toggle converts every input and result in place, so diameter reads in inches, length and head in feet, flow in gpm, velocity in ft/s and pressure drop in psi.

Should I use Darcy-Weisbach or Hazen-Williams?

This calculator uses Darcy-Weisbach with the Colebrook-White friction relationship, evaluated by the explicit Churchill correlation, which is valid for any Newtonian liquid in any flow regime. Hazen-Williams is a water-only empirical fit and has its own Hazen-Williams calculator on this site.

Can I use it for compressed air or other gases?

No. The fluid presets are all liquids and the physics is incompressible, so gas lines are out of scope here. Compressed air and other gas networks run on the compressible solver in the Studio.

Can I add bends, valves and fittings?

Not on this page, which models one straight pipe of uniform bore. Minor (fitting) losses and full networks with branches, pumps and valves are handled in the Studio, as in the supply line with a fitting example.

Is this the Darcy or the Fanning friction factor?

Darcy. The Darcy factor is four times the Fanning factor, so make sure any value you compare uses the same convention.

References

The methods on this page are not ours, and you should be able to check them at the source.

• Colebrook, C. F. (1939), "Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws", Journal of the Institution of Civil Engineers. doi.org/10.1680/ijoti.1939.13150
• Moody, L. F. (1944), "Friction factors for pipe flow", Transactions of the ASME. ASME Digital Collection
• Churchill, S. W. (1977), "Friction-factor equation spans all fluid-flow regimes", Chemical Engineering, Vol. 84, No. 24, pp. 91-92. This is the explicit correlation the calculator and the Studio evaluate.
• Crane Co., Technical Paper No. 410: Flow of Fluids Through Valves, Fittings and Pipe, the published source for the class of roughness values and design-velocity bands quoted above. Those are indicative tabulations rather than checked values, so verify the condition of your own pipe. tp410.com
• White, F. M., Fluid Mechanics, McGraw-Hill, for the derivation and the water property table.

Related

• Reynolds number calculator
• Darcy friction factor calculator
• Pipe velocity calculator
• Pump power calculator
• Rectangular duct pressure drop calculator
• Building a network with fittings, pumps or branches? Open the Studio.