Boneyard Tools

Darcy-Weisbach Head Loss Calculator

This calculator applies the Darcy-Weisbach equation to a full pipe running at steady flow. Type the Darcy friction factor, the pipe length, the inside diameter and the mean velocity in SI units, and it returns the friction head loss in metres of fluid. Tick the density box and it also converts that head into a pressure drop in pascals.

How to calculate Darcy-Weisbach head loss

  1. Enter the Darcy friction factor f, a dimensionless value read from a Moody chart or a Colebrook style correlation.
  2. Enter the pipe length in metres and the inside diameter in metres.
  3. Enter the mean flow velocity in metres per second.
  4. Leave the density box ticked and enter the fluid density in kg/m3 to also get the pressure drop, or untick it for head loss only.
  5. Read the head loss card in metres and the pressure drop card in pascals, then copy the result.

Examples

Water in a 100 m pipe with density on

f = 0.02, L = 100 m, D = 0.1 m, v = 3 m/s, density = 1000 kg/m3
head loss = 9.177445917 m, pressure drop = 90000 Pa

Larger main with a real water density

f = 0.025, L = 200 m, D = 0.15 m, v = 1.5 m/s, density = 998 kg/m3
head loss = 3.823935799 m, pressure drop = 37425 Pa

Head loss only, density box unticked

f = 0.018, L = 50 m, D = 0.05 m, v = 2 m/s
head loss = 3.670978367 m, pressure drop not available

Frequently asked questions

What equation does this calculator use?

Head loss equals f times the length over diameter ratio times velocity squared, all divided by two times g, where g is standard gravity 9.80665 m/s2. When you supply a density, the pressure drop is density times g times that head loss, which is the same as f times L over D times density times velocity squared over two.

What units do the inputs and outputs use?

The calculator is metric. Length and diameter are in metres, velocity is in metres per second and density is in kg/m3. Head loss comes back in metres of the flowing fluid and the pressure drop in pascals. Convert your data to these units first, for example millimetres of pipe bore to metres.

Where do I get the friction factor?

The friction factor f is an input, not something the tool derives. Read it from a Moody chart, or compute it from the Colebrook equation or the explicit Swamee-Jain approximation using the Reynolds number and the relative roughness of the pipe wall.

What is the difference between head loss and pressure drop?

Head loss is the lost energy expressed as a height of the fluid column in metres, independent of what fluid it is. Multiplying by density and g scales that height into a pressure drop in pascals, so a metre of head is a bigger pressure in water than in air.

Do I have to enter the density?

No. Untick the density box and the tool returns only the head loss in metres, showing the pressure drop as not available. Head loss alone is enough for a pump head calculation, while the pressure drop is handy when you size against a rated pressure.

Why does the head loss grow so fast with velocity?

The equation carries velocity squared, so friction loss tracks the kinetic energy of the flow. Doubling the velocity multiplies the head loss by four, which is why oversizing a pipe to slow the flow cuts pumping cost sharply.

Does it include fittings, bends and valves?

No. This is straight-pipe friction only. Elbows, tees, valves and entrances add minor losses that you account for separately, either with loss coefficients or by adding an equivalent length to the pipe length you enter here.

What are the limits on the inputs?

Every value must be a positive finite number greater than zero. Zero or negative length, diameter, velocity, friction factor or density is rejected, and the tool asks for numbers if a box is blank or non-numeric.

Is my data sent anywhere?

No. The whole calculation runs in your browser with plain arithmetic, so the pipe figures you type never leave your device and nothing is uploaded to a server.

Learn more

  • Finding the Darcy friction factor

    How the Darcy friction factor is read from a Moody chart or found with the Colebrook and Swamee-Jain equations from Reynolds number and roughness.

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