Calculate choked mass flow of a gas through a nozzle or orifice from pressure, temperature and throat size, or solve the throat size or pressure needed.
Choked Flow Formula
The calculator uses the ideal-gas choked-flow equation to find the maximum mass flow rate through the modeled nozzle or opening when the flow reaches sonic velocity at the throat. The ideal derivation uses steady, one-dimensional, isentropic flow and fixed specific heats. See NASA’s mass-flow derivation and isentropic relations. Cd is an empirical device correction, not part of the ideal derivation.
- ṁ = choked mass flow rate, usually in kg/s
- Cd = discharge coefficient
- A = orifice or throat area
- P1 = upstream absolute stagnation (total) pressure
- k = specific heat ratio, also written as γ
- R = specific gas constant
- T1 = upstream absolute stagnation (total) temperature
The specific gas constant is calculated from molar mass:
- R = specific gas constant in J/(kg·K)
- M = molar mass in g/mol
The calculator also checks whether the entered downstream pressure is low enough for choked flow:
- Pcrit = critical downstream absolute pressure
- P1 = upstream absolute stagnation (total) pressure
- k = specific heat ratio
The ideal sonic throat ratio is P*/P₀ = [2/(γ+1)](γ/(γ−1)). Applying it as a downstream choking threshold assumes the modeled nozzle/reservoir geometry; arbitrary valves or orifices may need a validated device model. This calculator requires entered downstream pressure, including zero for the ideal vacuum limit, and rejects a condition above the modeled choking threshold. It does not report a nonchoked flow rate or standard volumetric flow.
Typical Gas Properties for Choked Flow
Use gas-specific values when available. The values below and widget presets are fixed approximations near room temperature; they are not temperature-dependent property tables. Use verified properties at your upstream stagnation condition. NASA explains the temperature dependence of specific heats.
| Gas | Specific Heat Ratio, k | Molar Mass, M |
|---|---|---|
| Air | 1.40 | 28.97 g/mol |
| Nitrogen | 1.40 | 28.01 g/mol |
| Oxygen | 1.40 | 32.00 g/mol |
| Carbon dioxide | 1.29 | 44.01 g/mol |
| Helium | 1.66 | 4.00 g/mol |
| Hydrogen | 1.41 | 2.016 g/mol |
| Methane | 1.31 | 16.04 g/mol |
Critical Pressure Ratios
Choked flow occurs when the downstream absolute pressure is at or below the critical pressure shown by the ratio below.
| Specific Heat Ratio, k | Critical Ratio Pcrit / P1 | Meaning |
|---|---|---|
| 1.20 | 0.564 | Choked if downstream pressure is 56.4% of upstream pressure or lower |
| 1.30 | 0.546 | Common range for some heavier gases |
| 1.40 | 0.528 | Typical for air, nitrogen, and oxygen |
| 1.66 | 0.488 | Typical for monatomic gases such as helium |
Example Problems
Example 1: Air through a 0.01 in² orifice
Suppose you enter these values:
- Upstream pressure: 100 psi(a)
- Downstream pressure: 40 psi(a)
- Temperature: 70°F
- Specific heat ratio: 1.40
- Molar mass: 28.97 g/mol
- Discharge coefficient: 0.98
- Orifice area: 0.01 in²
For air with k = 1.40, the critical pressure ratio is about 0.528, so the critical downstream pressure is about 52.8 psi(a). Since 40 psi(a) is below that value, the flow is choked. The maximum choked mass flow is approximately 0.01027 kg/s, using the listed custom molar mass and assumed Cd. With the Air preset’s slightly different molar mass, it is approximately 0.01027045 kg/s.
Example 2: Air with a downstream pressure check
Suppose you enter these values:
- Upstream stagnation pressure: 10 bar(a)
- Downstream pressure: 1 bar(a)
- Temperature: 20°C
- Specific heat ratio: 1.40
- Molar mass: 28.97 g/mol
- Discharge coefficient: 0.98
- Orifice area: 10 mm²
The pressure ratio is 0.1, below the modeled critical ratio of approximately 0.52828. With the listed custom gas properties and assumed Cd, the choked mass-flow estimate is approximately 0.0231344 kg/s.
FAQ
Does downstream pressure affect the choked flow result?
Once flow is choked, lowering downstream pressure further does not increase the ideal choked mass flow rate. In this calculator, downstream pressure is used only to check whether choking occurs. The actual choked-flow equation uses upstream pressure, upstream temperature, gas properties, discharge coefficient, and area.
Should pressure be entered as gauge pressure or absolute pressure?
Use absolute pressure. Choked-flow equations depend on absolute pressure ratios and absolute gas density. If you have gauge pressure, convert it to absolute pressure before entering it. For example, 100 psig is about 114.7 psi(a) at sea-level atmospheric pressure.
What discharge coefficient should you use?
The discharge coefficient accounts for losses and non-ideal flow through the opening. The default Cd=1 represents an ideal opening. Use a measured or manufacturer-validated coefficient for the actual geometry and regime. The example’s Cd=0.98 is an explicit assumption, not a general recommendation. This tool does not certify safety-valve capacity or replace a real-gas, two-phase or piping model.
