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Head loss in a pipe, with the Darcy-Weisbach equation

Flow velocity, Reynolds number, the friction factor from an explicit approximation, the friction head loss, the pressure drop and the hydraulic power needed, for water in a 150 mm pipe.

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Darcy-Weisbach pipe flow head loss calculated in Equation Pad.

The calculation

Q := 0.025 m^3/s
D := 150 mm
L_p := 120 m
nu := 1.0e-6 m^2/s
e_r := 0.05 mm
rho := 1000 kg/m^3
A_p := pi*D^2/4 = mm^2
v := Q/A_p = m/s
Re := v*D/nu =
f := 0.25/(log10(e_r/(3.7*D) + 5.74/Re^0.9))^2 =
h_f := f*L_p/D*v^2/(2*g) = m
dp := rho*g*h_f = kPa
P_pump := rho*g*Q*h_f = kW

Results for these inputs

  • Velocity 1.41 m/s, Reynolds number 212 000 (turbulent).
  • Friction factor 0.0179.
  • Head loss 1.46 m over 120 m, pressure drop 14.3 kPa.
  • Hydraulic power 0.36 kW.

How it works

hf = f·(L/D)·v²/(2g), with the friction factor from the explicit Swamee–Jain form of the Colebrook relation. g is built in as 9.80665 m/s². Pressure drop is ρ·g·hf and hydraulic power ρ·g·Q·hf.

These calculations use classical textbook mechanics, not a design code. For design, use the method, factors and checks that apply to your work and have the result checked by a competent person.

Size a pipe

Find the diameter for a given head loss with root or solve, or tabulate several diameters in a spreadsheet with units and plot the head loss.

Questions

How is head loss in a pipe calculated?

With the Darcy-Weisbach equation, h_f = f·(L/D)·v²/(2g), where f is the friction factor from the Reynolds number and the relative roughness.

Which friction factor formula is used?

The explicit Swamee–Jain approximation, f = 0.25/[log10(ε/3.7D + 5.74/Re^0.9)]², valid for turbulent flow.

Also used for

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