Enter Engineering Inputs
Use absolute pressures for both upstream and downstream conditions.
Example Data Table
These sample engineering cases show how the calculator behaves for different gases, areas, and pressure ratios.
| Scenario | Gas | P0 | Pb | T0 | Area | Cd | Regime | Mass Flow | Critical Pb |
|---|---|---|---|---|---|---|---|---|---|
| Plant air header | Air | 700.00 kPa | 300.00 kPa | 320.00 K | 2.50 cm2 | 0.980 | Choked / critical flow | 0.38750 kg/s | 369.797 kPa |
| Nitrogen purge line | Nitrogen | 900.00 kPa | 500.00 kPa | 305.00 K | 1.20 cm2 | 0.950 | Subcritical compressible flow | 0.23312 kg/s | 475.454 kPa |
| Helium test nozzle | Helium | 1,200.00 kPa | 250.00 kPa | 295.00 K | 80.00 mm2 | 0.970 | Choked / critical flow | 0.08627 kg/s | 585.701 kPa |
Formula Used
(Pb / P0)critical = (2 / (k + 1))k / (k - 1)
ṁ = Cd × A × P0 × √[(k / (Z × R × T0)) × (2 / (k + 1))(k + 1) / (k - 1)]
ṁ = Cd × A × P0 × √[(2k / (Z × R × T0 × (k − 1))) × ((Pb/P0)2/k − (Pb/P0)(k+1)/k)]
T* = T0 × [2 / (k + 1)]P* = P0 × (2 / (k + 1))k / (k − 1)
This calculator assumes one-dimensional compressible gas flow with upstream stagnation conditions, a user-defined discharge coefficient, and a real-gas correction using compressibility factor Z.
When the downstream pressure falls below the critical threshold, the model reports choked flow. Lowering back pressure further will not increase mass flow unless upstream conditions or area change.
How to Use This Calculator
- Choose a gas preset or select custom to enter your own gas properties.
- Enter upstream and downstream absolute pressures using the desired units.
- Provide stagnation temperature, throat or orifice area, discharge coefficient, and gas constants.
- Click Calculate Critical Flow to display the result directly below the header.
- Review the flow regime, mass flow, critical back pressure, density, velocity, and the Plotly chart.
- Use the CSV or PDF buttons to export the calculated result summary.
FAQs
1) What is critical flow?
Critical flow is the choked condition where gas reaches sonic speed at the controlling section. Below that back pressure, mass flow no longer rises with additional downstream pressure reduction.
2) Why must I use absolute pressure?
Compressible flow equations depend on true thermodynamic pressure, not gauge pressure. Convert gauge values to absolute before entry or the pressure ratio and flow results will be wrong.
3) What does the discharge coefficient change?
The discharge coefficient corrects ideal flow to better match real hardware losses. Lower Cd values reduce mass flow and mass flux for the same pressure, area, and temperature conditions.
4) Can this calculator be used for liquids?
No. The model is designed for compressible gas discharge. Liquid choking and cavitation require different relationships, property data, and sometimes two-phase flow methods.
5) Why does the flow stop increasing after choking?
Once sonic velocity forms at the control section, information from downstream cannot propagate upstream through that point. The discharge becomes limited by upstream stagnation conditions and area.
6) What is the compressibility factor Z?
Z adjusts ideal-gas behavior for real-gas deviation. A value near 1 suits many moderate conditions, while higher-pressure systems may require property-based Z estimates.
7) Which gas constant should I enter?
Enter the specific gas constant in J/kg·K for the selected gas. If you use a preset, the calculator fills a typical value automatically.
8) Is this enough for final nozzle sizing?
It is a strong screening and checking tool, but final design may still need detailed geometry, friction, heat transfer, real-gas properties, standards compliance, and validated test data.