Pipe flow and pressure drop calculator

Work out the pressure drop and head loss for a liquid flowing in a circular pipe, or turn the question around and find the flow that a given available head will drive. The calculator uses the Darcy-Weisbach equation with the Colebrook-White friction factor, the same physically based method used inside 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 9.81 m/s^2 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 (Re < 2300): f = 64 / Re.
• 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 is solved iteratively (the Moody chart is its graphical form). The explicit Swamee-Jain equation approximates it to within about 1 per cent and is a fine starting guess. Fluid Network Studio (and this calculator) evaluate it with the Churchill (1977) correlation, an explicit form that reproduces Colebrook-White across all flow regimes.

Citation: Darcy-Weisbach; Colebrook, C. F. (1939); Moody, L. F. (1944). See any standard fluid mechanics text (for example White, Fluid Mechanics).

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 manual density (kg/m^3) and kinematic viscosity (m^2/s).
• Internal diameter D (mm).
• Length L (m).
• Absolute roughness epsilon (mm), with material presets (for example commercial steel about 0.045 mm, PVC about 0.0015 mm, concrete 0.3 to 3 mm).
• Mode A: flow Q (L/s), to find head loss and pressure drop.
• Mode B: available head (m), to find the flow.

Outputs

• Mean velocity (m/s) and Reynolds number, with the flow regime.
• Darcy friction factor.
• Head loss (m) and pressure drop (kPa and bar).
• In Mode B, the resulting flow (L/s).

Worked example

Water at 20 degrees C (density 998.2 kg/m^3, kinematic viscosity 1.004 x 10^-6 m^2/s) 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 = 2.55 m/s.
2. Re = 2.55 x 0.1 / 1.004e-6 = 253,700 (turbulent).
3. Relative roughness epsilon/D = 0.045/100 = 4.5 x 10^-4; Colebrook-White gives f = 0.0182.
4. h_f = 0.0182 x (50/0.1) x (2.55^2 / (2 x 9.81)) = 3.00 m.
5. dp = 998.2 x 9.81 x 3.00 = 29.4 kPa.

Reverse (Mode B): a 150 mm steel pipe, 200 m long, with 10 m of available head drives about 52.9 L/s (velocity 2.99 m/s, Re about 448,000, f = 0.0164).

Frequently asked questions

Is this the Darcy or the Fanning friction factor?

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

What roughness should I use?

Use the absolute roughness for the pipe material and condition. Typical values: commercial steel about 0.045 mm, drawn tubing about 0.0015 mm, PVC about 0.0015 mm, ductile iron about 0.26 mm; older or fouled pipe is rougher.

Can I add bends and valves?

Not on this single-pipe page. Minor (fitting) losses and full networks are handled in the Studio.

Related

• Reynolds number calculator
• Darcy friction factor calculator
• Pipe velocity calculator
• Building a network with fittings, pumps or branches? Open the Studio.