Pipe Flow Calculator
Solve flow rate Q and velocity from head loss or pressure drop in a full pressurized pipe — Darcy–Weisbach with the iterative Colebrook–White friction factor. Or run it in reverse to size the pipe diameter for a target flow. SI + US units.
Energy lost to wall friction along the pipe, expressed as a fluid column. ΔP = ρ·g·hf.
Results
How it works
For a pipe running completely full under pressure, the mean velocity follows from the Darcy–Weisbach equation rearranged for velocity:
v = √( 2·g·hf·d / (f·L) ) and Q = A·v = (π·d²/4)·vThe catch: the Darcy friction factor f itself depends on the velocity through the Reynolds number Re = ρ·v·d / μ:
1/√f = −2·log10( ε/3.7d + 2.51/(Re·√f) ) (Colebrook–White, iterated)This circular dependency is resolved by fixed-point iteration — guess f, compute v, recompute Re and f, repeat until v stops changing (converges to better than 1e-12). Laminar flow (Re < 2300) uses the exact f = 64/Re; the 2300–4000 transitional band blends both.
Pipe roughness table
Absolute roughness ε for common pipe materials. Rougher pipe → higher f → less flow for the same head loss.
| Material | ε (mm) |
|---|---|
| PVC / plastic, copper (drawn) | 0.0015 |
| Stainless steel | 0.002 |
| Commercial steel | 0.045 |
| Galvanized iron | 0.15 |
| Cast iron | 0.26 |
| Concrete | 0.30 |
Worked example
100 m of 100 mm commercial-steel pipe carrying water at 20 °C, with 3.16 m of head loss:
| Quantity | Value |
|---|---|
| Flow rate Q | 14.28 L/s (0.01428 m³/s, 226 GPM) |
| Mean velocity v | 1.82 m/s (5.96 ft/s) |
| Reynolds number | 181,110 — turbulent |
| Friction factor f (Colebrook) | 0.0187 |
| Pressure drop ΔP | 30.9 kPa (4.49 psi) |
Scope boundary
This tool solves flow rate Q from a known head loss / pressure drop in a full pressurized pipe, with the friction factor from the iterative Colebrook–White equation. It is not:
- The Darcy–Weisbach head loss calculator — that one solves the opposite direction: head loss from a known flow rate or velocity (plus minor losses).
- The open-channel flow calculator — for partially filled pipes, ditches and channels via Manning's equation.
- The orifice flow calculator — for local restrictions (orifice plates) via the discharge coefficient Cd.
Frequently asked questions
What does this pipe flow calculator compute?
It solves the flow rate Q (and mean velocity v) in a completely filled, pressurized circular pipe from a known head loss or pressure drop, using the Darcy–Weisbach equation with the friction factor f from the iterative Colebrook–White equation. It also reports Reynolds number, flow regime, friction factor and pressure drop, and can run in reverse to find the pipe diameter for a target flow rate.
How is the Darcy friction factor calculated?
For laminar flow (Re below 2300) it uses f = 64/Re. For turbulent flow (Re above 4000) it iterates the Colebrook–White equation 1/√f = −2·log10(ε/3.7d + 2.51/(Re·√f)) starting from the explicit Haaland approximation until f stops changing. Between Re 2300 and 4000 it blends the laminar and turbulent values.
What is the difference between laminar and turbulent flow?
Laminar flow (Re below 2300) moves in smooth parallel layers with low friction loss. Turbulent flow (Re above 4000) mixes chaotically and loses more energy to friction. Between 2300 and 4000 is the transitional zone where the flow is unstable.
Which units are supported?
SI and US customary. Enter diameter in mm or inches, length in m or ft, head loss in m or ft of fluid, pressure drop in kPa or psi, and flow rate in L/s or GPM. All physics is computed in SI internally and converted for display.
What roughness value should I use for my pipe?
Typical absolute roughness ε: commercial steel 0.045 mm, galvanized iron 0.15 mm, cast iron 0.26 mm, concrete 0.3 mm, PVC and copper 0.0015 mm, stainless steel 0.002 mm. Smoother pipe means a lower friction factor and higher flow for the same head loss. You can also enter a custom value.
How is this different from the Darcy–Weisbach head loss calculator?
They solve opposite directions of the same equation. This tool finds the flow rate Q from a known head loss or pressure drop. The Darcy–Weisbach calculator at nrtechstudio.com/tools/darcy-weisbach/ finds the head loss from a known flow rate or velocity.
Can it handle open channels like rivers or gutters?
No. This tool assumes a pipe running completely full under pressure. For partially filled pipes, ditches and channels, use the open-channel flow calculator at nrtechstudio.com/tools/open-channel-flow/, which uses Manning's equation.
What about flow through an orifice or restriction?
Local restrictions need a different model based on the discharge coefficient Cd. Use the orifice flow calculator at nrtechstudio.com/tools/orifice-flow/ for orifice plates and short restrictions instead of this long-pipe friction tool.
Why does the calculator iterate instead of solving directly?
The friction factor f depends on Reynolds number, which depends on velocity, which depends on f through the head loss equation. This circular dependency is resolved by fixed-point iteration: guess f, compute velocity, recompute f, and repeat until the velocity stops changing.
How does the reverse solver find pipe diameter?
Given a target flow rate Q and allowable head loss, head loss decreases strictly as diameter grows, so exactly one diameter matches. The tool brackets it between 0.1 mm and 10 m and bisects the interval 200 times, which recovers the diameter to far better than engineering tolerance.
What is the difference between head loss and pressure drop?
Head loss hf is energy loss expressed as metres (or feet) of the flowing fluid; pressure drop ΔP is the same loss expressed as force per area, ΔP = ρ·g·hf. The tool accepts either input and reports both.
What assumptions and limits apply?
Steady, incompressible, Newtonian flow in a straight circular pipe running full, with constant roughness and no fittings, valves or elevation change. Do not use it for gases at high Mach number, partially filled pipes, slurries, or systems where minor losses dominate — the answers will be wrong.
How do I convert the results to GPM or ft/s?
Results are shown in both systems automatically: flow rate in m³/s, L/s, L/min and GPM; velocity in m/s and ft/s; diameter in mm and inches. 1 GPM equals 6.30901964e-5 m³/s.
How accurate is the Colebrook–White iteration?
The fixed-point iteration converges to better than 1e-12 in f for all practical Reynolds numbers and roughness values, seeded with the Haaland explicit approximation which is already within about 2 percent. The remaining uncertainty comes from your inputs — especially the roughness estimate — not from the math.
Free tool by NRTechStudio