Instantly determine laminar, transitional, turbulent, or critical flow behavior today. Auto-fill water, air, and oil. See key numbers above the form after calculating once.
| Case | Key metric | Value | Regime |
|---|---|---|---|
| Pipe (Water) | Re | 50736 | Turbulent |
| Pipe (Air) | Re | 106431 | Turbulent |
| Channel | Fr | 0.54 | Subcritical |
| Channel | Fr | 1.814 | Supercritical |
For internal flow, the Reynolds number links inertia to viscosity. The calculator applies Re = ρVDh/μ with standard thresholds: Re < 2300 laminar, 2300–4000 transitional, and > 4000 turbulent. These bands help predict velocity-profile shape, mixing rate, and sensitivity to roughness. When flow rate is entered, velocity is derived from Q/A to keep calculations consistent across geometries.
For free-surface flow, the Froude number compares velocity to gravity-wave speed: Fr = V/√(gDh). Subcritical flow (Fr < 1) is deeper and wave-dominated, while supercritical flow (Fr > 1) is shallow, fast, and can form hydraulic jumps. The calculator flags values near Fr ≈ 1 as critical, a practical zone where energy and depth respond strongly to disturbances. For rectangular channels, an additional open-channel Reynolds estimate is provided for context.
Density and dynamic viscosity drive both Re and head-loss outputs. Water near room temperature typically sits around ρ ≈ 998 kg/m³ and μ ≈ 1.0×10⁻³ Pa·s, while air is about ρ ≈ 1.2 kg/m³ and μ ≈ 1.8×10⁻⁵ Pa·s. The tool also reports kinematic viscosity ν = μ/ρ, which is useful when comparing fluids of different densities. Because μ changes with temperature, using a representative operating temperature improves regime identification, especially for oils or warm water systems.
Noncircular passages are handled using hydraulic diameter Dh = 4A/P, allowing consistent Re estimates for rectangular ducts and annuli. For pipe head loss, the tool computes relative roughness ε/Dh and estimates the Darcy friction factor using laminar theory, a turbulent approximation, or a blended transitional value. With length L provided, it evaluates hf = f(L/Dh)(V²/2g) and pressure drop ΔP = ρghf, supporting design checks.
Use the example table to benchmark your inputs before modeling a new case. Confirm units, verify that area and hydraulic diameter are positive, and use roughness for the material. If Re sits near 2300–4000, rerun with small property changes to understand sensitivity. After calculating, export CSV for audit trails or PDF for field reports. Re-running with alternate properties helps quantify uncertainty and supports clear repeatable documentation.
1) What does “transitional” mean for pipe flow?
It indicates Reynolds numbers between about 2300 and 4000, where laminar and turbulent behavior can coexist. Small disturbances, fittings, or property changes can move the flow toward either regime, so treat results as sensitivity guidance.
2) Why is my open-channel result based on Froude number?
Free-surface stability depends on the balance between velocity and gravity-wave speed. Froude number captures that balance, separating subcritical (Fr<1), critical (≈1), and supercritical (Fr>1) behavior relevant to hydraulic jumps and depth control.
3) How should I pick roughness for the friction factor?
Use a material-appropriate estimate or a measured value. Relative roughness ε/Dh affects turbulent resistance strongly, but has minimal impact in laminar flow. If uncertain, run smooth and conservative rough cases to bracket head-loss outcomes.
4) Can I enter flow rate instead of velocity?
Yes. For supported geometries, the calculator converts discharge to velocity using V=Q/A. For custom hydraulic diameter cases, provide velocity directly because area is not derived automatically.
5) Why do my results change when I adjust fluid temperature?
Viscosity is temperature dependent, especially for oils and warm water. Since Reynolds number scales inversely with μ, a lower viscosity increases Re and can shift the predicted regime and friction losses. Use operating conditions for best alignment.
6) What do the CSV and PDF exports include?
Exports use your most recent calculation stored in the session. They include the selected mode, key inputs, and computed outputs such as Re or Fr, regime classification, and optional head loss and pressure drop for pipe cases.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.