Model turbulent flow in pipes using standard relations. Compare Colebrook, Haaland, and Swamee-Jain friction predictions. Export results for reports, designs, and quick checks today.
Enter geometry, fluid properties, and either flow rate or mean velocity. Choose a friction factor model for turbulent regime and include optional minor losses.
This calculator uses the Darcy–Weisbach approach for steady, incompressible, fully developed pipe flow:
A = πD² / 4V = Q / ARe = ρVD / μΔP_major = f (L/D) (ρV²/2)ΔP_minor = K (ρV²/2)h = ΔP / (ρg)For turbulent regimes, the Darcy friction factor f is estimated using the selected model (Colebrook-White, Haaland, Swamee-Jain, or Churchill) based on relative roughness ε/D and Reynolds number.
These sample cases illustrate typical turbulent water flow conditions.
| Case | D (mm) | L (m) | Q (L/s) | ε (mm) | ρ (kg/m³) | μ (cP) | ΣK | Model |
|---|---|---|---|---|---|---|---|---|
| 1 | 100 | 50 | 20 | 0.045 | 998 | 1.002 | 2 | Colebrook |
| 2 | 50 | 120 | 6 | 0.015 | 1000 | 1.00 | 8 | Haaland |
| 3 | 200 | 300 | 55 | 0.26 | 997 | 0.90 | 1 | Churchill |
Turbulent pipe flow analysis estimates the energy lost to friction and fittings in steady internal flow. When Reynolds number rises above about 4000, eddies increase dissipation and pressure drop becomes a key design constraint. This calculator converts your geometry and fluid properties into velocity, Reynolds number, friction factor, pressure drop, head loss, and power.
Inputs are diameter D, length L, roughness epsilon, density rho, and viscosity mu, plus either flow rate Q or mean velocity V. The tool computes area A = pi D^2/4 and links Q and V through V = Q/A. It also reports relative roughness epsilon/D, a dimensionless indicator of how wall texture influences friction.
Reynolds number is Re = rho V D / mu. For Re below 2000, flow is typically laminar and the calculator uses f = 64/Re. Between 2000 and 4000, flow may be transitional; friction factor can fluctuate with disturbances. For Re well above 4000, empirical turbulent friction models apply.
Roughness can change with material and age. Smooth plastic or drawn tubing may behave nearly hydraulically smooth, while scaled or corroded steel can produce higher epsilon/D. At high Re, friction factor becomes less sensitive to viscosity and more sensitive to epsilon/D, so older pipes can require substantially higher pumping head.
Colebrook-White is a common reference relation but it is implicit, so this calculator solves it iteratively. Haaland and Swamee-Jain are explicit approximations that are fast and usually close for many engineering ranges. Churchill is a smooth correlation that works across regimes and roughness levels. Comparing models helps you judge uncertainty; typical Darcy f values often fall roughly between 0.008 and 0.08.
Major loss uses Darcy-Weisbach: DeltaP_major = f (L/D) (rho V^2/2). Minor loss uses DeltaP_minor = sumK (rho V^2/2). If you have several fittings, sumK can be significant; for example, a sharp entrance and exit plus a few elbows can produce sumK of 2 to 10 or more. Total head loss is h = DeltaP/(rho g), reported in meters for direct pump sizing.
Hydraulic power is P_h = DeltaP_total * Q. Because DeltaP scales with V^2 and Q scales with V, power often grows near V^3, so small velocity reductions can save large energy. Shaft power divides by efficiency; using 0.60 to 0.85 is common for preliminary estimates. Use power to compare diameter options and lifecycle cost, not only initial pipe cost.
Confirm diameter is the internal diameter and viscosity is dynamic viscosity, not kinematic. If Re is close to transitional, apply a margin or validate with test data. For long pipelines, focus on L/D and roughness control; for compact skids, fittings and valves may dominate, so estimate sumK carefully.
Colebrook-White is a standard reference. Haaland or Swamee-Jain are fast explicit options for quick sizing. Churchill is a robust all-range correlation. If you are unsure, compare two models and design with a conservative margin.
Between roughly Re = 2000 and 4000, the flow can switch between laminar and turbulent depending on disturbances, fittings, and inlet conditions. Friction factor is less predictable, so treat results as approximate and validate when accuracy matters.
Pressure drop is reported in pascals. Head loss is the same energy loss expressed as an equivalent fluid column height in meters: h = DeltaP/(rho g). Head is convenient for pump curves and system head calculations.
Sum the K values of each fitting and component in the line: entrances, exits, elbows, valves, reducers, and filters. Manufacturer datasheets and standard handbooks provide typical K values. Add them to capture compact system losses.
This calculator assumes incompressible flow with constant density. For gases with large pressure changes, density varies along the pipe and compressible flow methods are needed. It can be used for small pressure drops where density changes are negligible.
It assumes a constant dynamic viscosity mu. Many non-Newtonian fluids require an apparent viscosity model and modified Reynolds number definitions. Use this tool only if you can justify a constant mu over the shear-rate range of your system.
Losses determine hydraulic power P_h = DeltaP * Q. Efficiency converts that hydraulic demand into shaft power for motor sizing: P_shaft = P_h/eta. Including eta helps translate fluid losses into electrical and mechanical requirements.