Calculator Inputs
Example Data Table
| Item | Example Value |
|---|---|
| Gas | Air |
| Upstream pressure P0 | 700 kPa(abs) |
| Back pressure Pb | 300 kPa(abs) |
| Upstream temperature T0 | 300 K |
| Specific heat ratio γ | 1.40 |
| Specific gas constant R | 287 J/kg·K |
| Discharge coefficient Cd | 0.98 |
| Throat diameter | 12 mm |
| Compressibility factor Z | 1.00 |
| Parallel nozzles | 1 |
| Expected regime | Choked |
| Approximate mass flow | 0.181049 kg/s |
| Approximate sonic velocity | 316.938 m/s |
Formula Used
This calculator applies standard compressible flow relations for gases flowing through a nozzle or restriction. The decision point is the critical pressure ratio.
1) Critical pressure ratio
(Pb / P0)critical = (2 / (γ + 1))^(γ / (γ - 1))
2) Choked mass flow rate
ṁ = Cd × A × P0 × sqrt[γ / (R × T0 × Z)] × (2 / (γ + 1))^((γ + 1) / (2 × (γ - 1)))
3) Subsonic mass flow rate when not choked
ṁ = Cd × A × P0 × sqrt[(2γ / (R × T0 × Z × (γ - 1))) × ((Pb/P0)^(2/γ) - (Pb/P0)^((γ + 1)/γ))]
4) Critical throat temperature and sonic velocity
T* = T0 × (2 / (γ + 1)), a* = sqrt(γ × R × T*)
Where Cd is discharge coefficient, A is throat area, P0 is upstream absolute pressure, Pb is back pressure, T0 is upstream absolute temperature, γ is specific heat ratio, R is specific gas constant, and Z is compressibility factor.
How to Use This Calculator
- Enter the gas label for reporting clarity.
- Provide upstream absolute pressure and downstream back pressure.
- Enter upstream absolute temperature in Kelvin.
- Enter gas properties: specific heat ratio and specific gas constant.
- Enter discharge coefficient for the nozzle or restriction.
- Enter throat diameter, or directly enter throat area.
- Set compressibility factor to 1 for ideal-gas assumptions.
- Enter the number of identical parallel nozzles.
- Press the calculate button to view results above the form.
- Use the chart and export buttons for reporting.
FAQs
1) What is choked flow?
Choked flow occurs when gas velocity reaches Mach 1 at the throat. After that point, lowering downstream pressure no longer increases mass flow for the same upstream state and area.
2) Why must pressures be absolute?
Compressible flow equations use absolute thermodynamic pressure. Gauge pressure can produce wrong pressure ratios, wrong critical conditions, and incorrect mass flow predictions.
3) What does the discharge coefficient do?
The discharge coefficient corrects ideal flow for losses, vena contracta effects, and geometry imperfections. A lower value reduces predicted mass flow.
4) When should I override throat area?
Override area when the restriction is non-circular, already measured, or taken from manufacturer data. The area entry takes priority over diameter.
5) Can I use this for liquids?
No. This model is intended for gases under compressible flow conditions. Liquid choking and cavitation require different equations and assumptions.
6) What if my gas is not ideal?
Use a realistic compressibility factor Z when you have it. This adds a practical correction, but high-pressure real-gas work may still need a detailed equation of state.
7) Why does the chart flatten at low back pressure?
That flat region shows choking. Once the critical pressure ratio is crossed, mass flow becomes nearly constant for the same upstream pressure, temperature, and throat area.
8) Can I size multiple nozzles with this page?
Yes. Enter the number of identical parallel nozzles. The calculator multiplies single-nozzle mass flow to show the total delivered flow.