Darcy-Weisbach Friction Loss Calculator

Darcy-Weisbach Equation

The Darcy-Weisbach equation calculates the frictional head loss (or pressure drop) in a pipe due to fluid viscosity and pipe roughness. It is the most accurate and widely used pipe flow equation.

Head loss formula:

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

Pressure drop formula:

dP = f * (L/D) * (rho * v^2 / 2) [in Pascals]

Variables:

Reynolds number:

Re = v * D / nu

where nu = kinematic viscosity (m^2/s)

Friction factor f:

• Laminar (Re < 2300): f = 64/Re
• Transitional (2300-4000): flow is unstable: use caution
• Turbulent (Re > 4000): Swamee-Jain approximation: f = 0.25 / [log10(eps/(3.7D) + 5.74/Re^0.9)]^2

Where eps = pipe absolute roughness (m).

Common pipe roughness values:

• Smooth (PVC, glass): eps ≈ 0.0015 mm
• Commercial steel: eps ≈ 0.046 mm
• Cast iron: eps ≈ 0.26 mm
• Concrete: eps ≈ 1.0 mm

Key insight: Head loss scales with v^2, so doubling the flow velocity quadruples the friction loss. This makes reducing pipe velocity one of the most effective ways to cut pumping energy.

Why the diameter matters far more than the roughness

Designers agonize over pipe material and then pick the diameter off a price list, which is backwards. Hold the flow rate constant and velocity goes as 1/D^2, so the v^2 term alone gives 1/D^4, and the explicit L/D factor takes it to 1/D^5. Take 100 m of steel pipe carrying the flow that gives 2 m/s in a 50 mm bore: head loss is 9.0 m. Move to 65 mm and the same flow loses 2.4 m, a factor of 3.7. Staying at 50 mm and switching from cast iron to PVC is worth 43% on the friction factor, which is a genuinely large gain and still less than one pipe size buys you.

A note on the transitional band

Between Re 2300 and 4000 the flow cannot make up its mind, and no correlation is reliable there. This calculator carries the laminar 64/Re into that band, and you should read that number as the optimistic end, not a safe one. The two correlations disagree badly at the handover: for oil in a 50 mm pipe at Re 4000, laminar gives about 104 m of loss over 100 m of pipe and the turbulent formula gives about 271 m. Real systems drift in and out of turbulence in that range as temperature and flow wobble, so size the pump for the turbulent figure. Designing anything to sit permanently at Re 3000 is asking for unstable behavior, and the step you can see in the chart is exactly why.