Pipe Flow Calculator

The Pipe Flow Calculator tells you how a fluid behaves inside a circular pipe. Enter the pipe size, length, material, and fluid, and either a flow rate or a pressure drop — the tool returns the velocity, Reynolds number, friction factor, head loss, and pressure drop, with the Hazen-Williams and Darcy-Weisbach + Colebrook-White equations running side-by-side so you can compare. A live animation shows whether your flow is laminar, transitional, or turbulent.

What This Calculator Computes

The Two Equations

Darcy-Weisbach is the universal pipe-flow equation. It works for any liquid or gas, in any regime, and is the gold standard for engineering design:

\( h_f = f \cdot \dfrac{L}{D} \cdot \dfrac{V^2}{2g} \)

The friction factor \(f\) depends on Reynolds number and relative roughness. We use the Swamee-Jain explicit form of the Colebrook-White equation for turbulent flow, and \(f = 64 / Re\) for laminar.

Hazen-Williams is an empirical formula valid only for water near room temperature in turbulent flow. It uses a single roughness coefficient C:

\( h_f = \dfrac{10.67 \cdot L \cdot Q^{1.852}}{C^{1.852} \cdot D^{4.87}} \) (SI units)

It is faster to compute and accurate for water service mains, fire mains, and irrigation, but can drift 5–25% from Darcy-Weisbach outside its design range.

Pipe Material Roughness Reference

Recommended Velocity by Application

How to Use This Calculator

1. Pick your unit system — Imperial for US plumbing/civil work, Metric for everyone else.
2. Choose what to solve for — pressure drop from a known flow, or flow / velocity from a known pressure drop. The relevant input fields appear automatically.
3. Enter the pipe — actual inside diameter, length, and material. The material sets both Hazen-Williams C and absolute roughness for Darcy-Weisbach.
4. Enter the fluid — water at the closest temperature, or pick another preset (seawater, diesel, oil, glycerin, milk), or enter custom density and viscosity.
5. Pick the equation — keep "Auto" to see both methods compared, or pick a single equation if you know which one your code requires.
6. Press Calculate — the headline number is your answer; the side panel shows velocity, Reynolds number, friction factor, and head loss; the comparison table shows both methods; the animated visualization shows whether you are in laminar, transitional, or turbulent flow.

Frequently Asked Questions

What is the difference between Hazen-Williams and Darcy-Weisbach?

Darcy-Weisbach is the universal pipe-flow equation. Its friction factor f depends on Reynolds number and relative roughness, and it works for any liquid or gas in any regime. Hazen-Williams is an empirical formula valid only for water near room temperature in turbulent flow, using a single roughness coefficient C. It is fast but can drift 5–25% from the Darcy-Weisbach result outside its design range — use Darcy-Weisbach for design and Hazen-Williams for quick water-only checks.

What is Reynolds number and why does it matter?

Reynolds number Re equals velocity times diameter divided by kinematic viscosity. It tells you the flow regime: below 2300 is laminar (viscosity dominates, friction depends only on Re), above 4000 is turbulent (roughness matters), and between 2300 and 4000 is transitional and unstable. Designers usually keep water systems firmly in turbulent flow, where pressure drop is predictable.

How is pressure drop converted to head loss?

Head loss h_f and pressure drop ΔP are linked by ΔP = ρ·g·h_f. So one foot of water column ≈ 0.433 psi, and one metre of water column ≈ 9.81 kPa. The calculator converts both ways automatically once you pick the fluid.

Which roughness should I use for cast iron?

New asphalted cast iron is around 0.12 mm with C 130; plain new cast iron around 0.26 mm with C 110; old encrusted cast iron can reach 1.5 mm or more with C as low as 90. Pick the value that matches the actual pipe condition, because deposits and corrosion grow roughness over time.

Does the calculator include fittings and valves?

No. This calculator covers friction along straight pipe only. To include fittings, valves, expansions, and entrances, add their equivalent lengths to the pipe length, or compute the minor loss separately as K·V²/(2g) and add it to the result.

What is a typical maximum velocity for water in pipes?

Building water service usually targets 2–7 ft/s (0.6–2.1 m/s). Below 1 ft/s sediment can settle. Above 7 ft/s noise and erosion become problems, especially in copper and CPVC. Above 10 ft/s water hammer risk grows quickly. Industrial chilled water and main lines may go higher — check your design code.

Limitations & Disclaimer

This tool is intended for preliminary sizing, study, and feasibility checks of single-phase, incompressible, steady flow in straight circular pipes that are running full. It does not handle compressible flow, two-phase flow, partially full pipes (use Manning's equation), pulsating flow, slurries, or non-Newtonian fluids. For final design, follow your governing code — ASHRAE, AWWA, NFPA, ASME B31, ISO, or a professional engineer's review.