Total pressure drop
-Velocity
-Reynolds number
-Friction factor f
-All results
| Flow area | - |
| Dynamic pressure, ρv²/2 | - |
| Relative roughness, e / D | - |
| Flow regime | - |
| Friction loss in the pipe | - |
| Fitting (minor) losses | - |
| Elevation (static head) | - |
| Total pressure drop | - |
| Head loss (friction + fittings) | - |
| Hydraulic power lost to friction and fittings | - |
Method and equations
Steady, incompressible flow of a single liquid in a full round pipe. Every figure can be checked by hand.
| Quantity | Equation |
|---|---|
| Velocity | v = Q / A, A = π D² / 4 |
| Reynolds number | Re = ρ v D / μ |
| Laminar friction factor (Re < 2 300) | f = 64 / Re |
| Turbulent friction factor (Colebrook-White) | 1 / √f = −2 log10( (e/D) / 3.7 + 2.51 / (Re √f) ) |
| Friction loss (Darcy-Weisbach) | Δpf = f (L / D) ρ v² / 2 |
| Fitting losses | ΔpK = ΣK ρ v² / 2 |
| Elevation | Δpz = ρ g Δz |
| Total | Δp = Δpf + ΔpK + Δpz |
| Power lost | P = Q (Δpf + ΔpK) |
The Colebrook equation is solved by fixed-point iteration. Between Re 2 300 and 4 000 the flow is in transition: the calculator uses the larger of the laminar and turbulent friction factors and shows a warning. g = 9.80665 m/s².
Worked example: water at 20 °C, 300 L/min through 100 m of 50 mm steel pipe, K = 5
Area = π × 0.05² / 4 = 0.001963 m², so v = 0.005 / 0.001963 = 2.546 m/s. Re = 998.2 × 2.546 × 0.05 / 0.001002 = 126,841 (turbulent). With e = 0.045 mm, e/D = 0.0009 and Colebrook gives f = 0.0214. Dynamic pressure = 998.2 × 2.546² / 2 = 3.236 kPa. Friction loss = 0.0214 × (100 / 0.05) × 3.236 kPa = 138.2 kPa. Fittings = 5 × 3.236 = 16.18 kPa. Total = 154.4 kPa = 1.544 bar.
Questions
How do you calculate pressure drop in a pipe?
Use the Darcy-Weisbach equation: dp = f x (L / D) x (rho v^2 / 2), where f is the Darcy friction factor, L the pipe length, D the inside diameter, rho the fluid density and v the mean velocity v = Q / A. Add the minor losses from fittings, dp = K x rho v^2 / 2, and any static head, rho g dz. This calculator sums the three.
How is the friction factor found?
In laminar flow (Reynolds number below about 2 300) f = 64 / Re. In turbulent flow it comes from the Colebrook-White equation, 1 / sqrt(f) = -2 log10( (e/D) / 3.7 + 2.51 / (Re sqrt(f)) ), which is solved here by iteration. Between Re 2 300 and 4 000 the flow is in transition and any value is uncertain, so the calculator uses the higher of the laminar and turbulent values and warns you.
What pipe roughness should I use?
The presets are typical new-pipe values: drawn tubing about 0.0015 mm, commercial or welded steel about 0.045 mm, galvanized iron about 0.15 mm, cast iron about 0.26 mm, and concrete 0.3 to 3 mm. Old, corroded or scaled pipe can be several times rougher. Use the manufacturer figure when you have it.
What K value should I use for fittings?
Add up the K values of every fitting in the line. Typical turbulent-flow values are about 0.9 for a standard 90 degree elbow, 0.2 for a fully open gate valve, 10 for a fully open globe valve, 0.5 for a sharp-edged pipe entrance and 1.0 for an exit into a tank. K values vary with size, type and flow, so use your supplier's data for important lines.
What is a sensible velocity in a pipe?
As a rough guide, water suction lines run at 1 to 2 m/s (3 to 6 ft/s), water discharge and process lines at 2 to 3 m/s (6 to 10 ft/s), and hydraulic oil pressure lines at 3 to 6 m/s (10 to 20 ft/s). Higher velocities raise pressure drop, noise, erosion and water hammer risk.
Does this work for gases and air?
Only for low pressure drops, where the density barely changes along the pipe (a few percent of the absolute pressure). For compressed air or long gas lines the density changes with pressure, so use a compressible-flow method instead.
What does this calculator not cover?
It covers steady, single-phase, incompressible flow in a full round pipe. It does not cover non-Newtonian fluids, two-phase flow, slurries, partly full pipes, pump curves, NPSH, water hammer or heat transfer. Check the pressure rating of the pipe and every fitting separately.
Background: Darcy friction factor explained (laminar, Colebrook, typical values).
Engineering aid for guidance. It covers steady, single-phase, incompressible flow in full round pipes and does not cover gases at large pressure drops, non-Newtonian fluids, two-phase flow, pumps, NPSH or water hammer. Verify critical designs.