| Case | Geometry | ρ (kg/m³) | μ (Pa·s) | Size (m) | V (m/s) | Re | Fr | Regime |
|---|---|---|---|---|---|---|---|---|
| A | Circular pipe | 998 | 0.001 | D=0.10 | 0.20 | 19,960 | 0.20 | Turbulent + Subcritical |
| B | Circular pipe | 1000 | 0.01 | D=0.05 | 0.30 | 1,500 | 0.43 | Laminar + Subcritical |
| C | Rectangular channel | 998 | 0.001 | b=1.00, y=0.40 | 2.50 | ~1,662,000 | 1.26 | Turbulent + Supercritical |
- Choose the system and geometry that match your case.
- Enter fluid density and dynamic viscosity in SI units.
- Select velocity or flow rate input mode.
- Provide the required dimensions for your geometry.
- Press Compute Regime to view results above the form.
- Use CSV or PDF buttons to export the latest run.
Reynolds and Froude framework for regime screening
This calculator classifies flow by combining Reynolds number and Froude number into one regime statement. Reynolds captures the balance of inertial and viscous forces using Re = ρVDh/μ. Froude captures inertia versus gravity using Fr = V/√(gD). Together, these indicators support rapid checks for viscosity dominance, turbulence, free-surface wave behavior, and rapid-flow risk.
How to interpret the regime map point
The plotted point uses a logarithmic Reynolds axis and a linear Froude axis. Vertical bands summarize laminar, transitional, and turbulent ranges, while horizontal bands represent subcritical, critical, and supercritical states. The narrow critical zone highlights conditions where small changes in discharge or depth can cause abrupt shifts. Use the combined label to communicate expected mixing, profile stability, and whether disturbances can travel upstream.
Geometry effects through hydraulic diameter and depth
For non-circular sections, hydraulic diameter Dh = 4A/P converts geometry into a comparable length scale for Reynolds calculations. Small changes in area or wetted perimeter can shift the classification near transition, especially when tolerances or fouling alter the wetted perimeter. For open rectangular channels, hydraulic depth D = A/T ties Froude to depth and top width, which is decisive for shallow or wide flows.
Applying the result to design decisions
Regime identification is most useful as an early engineering screen before detailed modeling. Laminar flow suggests strong temperature sensitivity and weaker mixing, affecting heat transfer and dispersion. Turbulent flow supports higher friction losses and stronger mixing, guiding roughness selection and loss correlations. Supercritical channel flow may need energy dissipation and careful lining selection; subcritical flow may be influenced by downstream controls and backwater. In transition, apply conservative allowances and consider multiple scenarios to avoid overstating certainty.
Data quality checks that improve confidence
Accurate classification depends on consistent SI units and representative fluid properties. Confirm viscosity at operating temperature, verify whether depth is wetted depth, and ensure geometry matches the wetted boundary. Cross-check computed velocity against measured discharge or equipment limits, then export CSV or PDF to document assumptions and compare scenarios. If your point sits near a boundary, repeat the run with upper and lower bounds of properties to quantify sensitivity and improve traceability.
1) Which inputs most strongly affect Reynolds number?
Re scales with density, velocity, and hydraulic diameter, and it decreases with viscosity. In practice, velocity and temperature-driven viscosity changes usually dominate the shift between laminar, transitional, and turbulent ranges.
2) Why is hydraulic diameter used for rectangular conduits?
Hydraulic diameter converts any wetted shape into an equivalent length based on area and wetted perimeter. It allows Reynolds calculations that are consistent across circular pipes, rectangular ducts, and partially wetted sections.
3) What does a Froude number near one mean?
Fr near 1 indicates critical conditions where flow depth and energy are highly sensitive. Small changes in discharge, slope, or roughness can push the system toward subcritical or supercritical behavior.
4) Can this tool replace detailed hydraulic or CFD analysis?
No. It is a fast screening and documentation aid. Use governing equations, calibrated loss models, and boundary conditions to design for pressure drop, depth profiles, stability, and safety margins.
5) How should I set density and viscosity for mixtures?
Prefer measured properties at operating temperature and composition. If estimates are necessary, use validated mixture correlations and record the source, temperature, and concentration so results remain traceable.
6) Why do results change between velocity mode and flow-rate mode?
They should match if inputs are consistent. Differences usually come from a dimension error, a geometry mismatch, or a flow rate that does not correspond to the stated velocity and cross-sectional area.