Pipe Pressure Drop Calculator (Darcy-Weisbach)

How is pipe pressure drop calculated?

Friction loss in straight pipe follows the Darcy-Weisbach equation: Δp = f × (L / d) × ρ × v² / 2, where f is the friction factor, L the pipe length, d the inside diameter, ρ the density and v the mean velocity. Losses in fittings such as elbows and valves are added on the same dynamic pressure through the sum of loss coefficients ΣK.

Reynolds number and flow regime

First find Re = ρ × v × d / μ. Below 2300 the flow is laminar and f = 64 / Re. Above 4000 it is turbulent: f depends on both the Reynolds number and the relative roughness (ε / d) and comes from the Colebrook-White equation. Since f appears on both sides, the equation is solved by iteration. The Moody chart is a plot of the same equation. In the transitional range between the two the flow is unstable.

Example

Water at 20 °C flows at 30 cubic metres per hour through new steel pipe with an 80 mm bore. The velocity is 1.66 m/s and the Reynolds number about 132 000, so the flow is turbulent. The friction factor is close to 0.020 and the pressure drop over 100 metres is about 0.34 bar, or 3.5 metres of water column.

Limits

The calculation covers incompressible fluids in full circular pipes. Roughness values are approximate figures for new pipe, and aged lines lose noticeably more. Elevation change, pump and equipment losses are added separately.