A pipe flow calculator for pressure drop and flow rate
This pipe flow calculator finds the pressure drop along a pipe for a given flow, or the flow a pipe can carry for the pressure you have. It uses the Darcy–Weisbach equation with the Colebrook friction factor for any liquid, the Hazen–Williams formula familiar to water engineers, and Manning’s equation for gravity drains and sewers running full or part full.
Enter flow in L/s, L/min, m³/h, US gpm or ft³/s, the pipe’s inside diameter and length, and the fittings in the line. Results include velocity, Reynolds number and flow regime, friction factor, head loss from friction and from fittings, and the pressure drop in kPa, bar, psi or metres of water. Water properties at 0–100 °C are interpolated from NIST data; for oils and other liquids you can type the density and viscosity.
How to use the Pipe Flow & Pressure Drop Calculator
- Choose Darcy–Weisbach, Hazen–Williams or Manning, and SI or US units.
- Pick Pressure drop from flow or Flow from pressure drop, then enter the flow or the pressure available.
- Enter the inside diameter, length and any elevation rise. For Darcy–Weisbach choose the fluid and the pipe material (or type the roughness).
- Open Fittings and minor losses and enter how many elbows, tees and valves the line has.
- For Manning, enter n, the slope and the depth ratio instead. Then copy the working if you need it.
Pipe Flow & Pressure Drop Calculator features
Colebrook, solved exactly
The implicit Colebrook equation is iterated to machine precision; Swamee–Jain is shown alongside.
Laminar to turbulent
Uses 64/Re below Re 2,300 and flags the uncertain transition zone.
Flow from pressure
Finds the flow for an available pressure drop, including fittings and elevation.
Three methods
Darcy–Weisbach for any liquid, Hazen–Williams for water, Manning for gravity flow, part-full included.
Sourced data
NIST water properties, Moody’s 1944 roughness values and FHWA culvert n values.
Darcy–Weisbach, Colebrook and Swamee–Jain
The Darcy–Weisbach equation gives the friction head loss as hf = f × (L/D) × V²/2g, and the pressure drop as Δp = ρ g (hf + hm + Δz), where hm = ΣK V²/2g covers fittings. The Reynolds number Re = ρVD/μ decides the regime. In laminar flow f = 64/Re; in turbulent flow the calculator solves C. F. Colebrook’s 1939 equation 1/√f = −2 log10(ε/3.7D + 2.51/(Re√f)), and shows P. K. Swamee and A. K. Jain’s 1976 explicit approximation f = 0.25/[log10(ε/3.7D + 5.74/Re0.9)]², which is within about 1% for 5,000 ≤ Re ≤ 10⁸.
Example: 3 L/s of water at 20 °C through 100 m of 50 mm commercial steel pipe flows at 1.53 m/s with Re ≈ 76,000. With ε = 0.046 mm, f ≈ 0.0225, the friction head is about 5.37 m and the pressure drop about 52.6 kPa (0.53 bar, 7.6 psi).
| Pipe material (Moody, 1944) | Roughness ε |
|---|---|
| Drawn tubing (copper, brass, glass); smooth plastic | 0.0015 mm |
| Commercial steel, wrought iron | 0.046 mm |
| Galvanised iron | 0.15 mm |
| Cast iron | 0.26 mm |
| Concrete | 0.3–3 mm |
| Riveted steel | 0.9–9 mm |
Hazen–Williams and Manning
Hazen–Williams is an empirical formula for water at ordinary temperatures: hf = 10.67 L Q1.852 / (C1.852 D4.87) in SI units, with C about 150 for plastic and 100 for old cast iron. It ignores viscosity, so use Darcy–Weisbach for hot water, other liquids or unusual velocities. To choose a diameter from a flow, the pipe size calculator is quicker.
Manning’s equation, V = (1/n) R2/3 S1/2 (1.486/n in US units), suits drains, sewers and culverts driven by slope. The FHWA’s Hydraulic Design of Highway Culverts (HDS-5, 2012) lists n = 0.009–0.011 for smooth PVC and 0.010–0.011 for concrete pipe, and uses 0.012 for smooth and 0.024 for corrugated culverts in design.
Related calculators
Size a pump for the head you found with the water pump HP calculator, convert units with the pressure converter, and look up hot-water and steam properties in the steam table calculator.
Pipe Flow & Pressure Drop Calculator FAQ
How do I calculate pressure drop in a pipe?
Use Darcy–Weisbach: Δp = f (L/D) ρV²/2, plus ΣK ρV²/2 for fittings and ρgΔz for any rise. The friction factor f comes from the Reynolds number and relative roughness via the Colebrook equation; this pipe flow calculator does all of it.
How do I use the pipe flow calculator in GPM?
Choose US units and US gpm as the flow unit, enter the inside diameter in inches and the length in feet, and choose psi for the pressure. The working converts to SI internally and back.
How do I find flow rate from pressure?
Choose “Flow from pressure drop” and enter the pressure available. The calculator searches for the flow whose friction, fitting and elevation losses use exactly that pressure.
When should I use Manning instead of Darcy–Weisbach?
Use Manning for gravity flow driven by slope, such as storm drains and sewers. Use Darcy–Weisbach or Hazen–Williams for pressurised pipes flowing full.
What is a good velocity for water in a pipe?
Many designers aim for roughly 0.6–2.5 m/s (2–8 ft/s) in water mains and building services; higher velocities add noise, erosion and water hammer.
Why does Colebrook need iteration?
The friction factor appears on both sides of the equation. The calculator iterates until it stops changing, which takes a handful of steps.