Calculate maximum choked flow for an ideal gas from upstream pressure, temperature, gas properties, orifice area, and discharge coefficient.
Choked Flow Formula
The calculator uses the ideal-gas choked-flow equation to find the maximum mass flow rate through an orifice or nozzle when the flow reaches sonic velocity at the throat.
\dot{m} = C_d A P_1 \sqrt{\frac{k}{R T_1}\left(\frac{2}{k+1}\right)^{\frac{k+1}{k-1}}}- \(\dot{m}\) = choked mass flow rate, usually in kg/s
- \(C_d\) = discharge coefficient
- \(A\) = orifice or throat area
- \(P_1\) = upstream absolute pressure
- \(k\) = specific heat ratio, also written as \(\gamma\)
- \(R\) = specific gas constant
- \(T_1\) = upstream absolute temperature
The specific gas constant is calculated from molar mass:
R = \frac{8314.462618}{M}- \(R\) = 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:
\frac{P_{crit}}{P_1} = \left(\frac{2}{k+1}\right)^{\frac{k}{k-1}}P_{crit} = P_1 \left(\frac{2}{k+1}\right)^{\frac{k}{k-1}}- \(P_{crit}\) = critical downstream absolute pressure
- \(P_1\) = upstream absolute pressure
- \(k\) = specific heat ratio
If \(P_2 \le P_{crit}\), the flow is choked. If \(P_2 > P_{crit}\), the flow is not choked at the entered pressures, but the calculator still reports the maximum choked flow that would occur if downstream pressure were reduced enough.
For standard volumetric outputs, the mass flow is converted using ideal-gas density at the selected standard condition:
\rho_{std} = \frac{P_{std}}{R T_{std}}Q_{std} = \frac{\dot{m}}{\rho_{std}}- \(\rho_{std}\) = gas density at the standard condition
- \(P_{std}\) = standard pressure, 101325 Pa
- \(T_{std}\) = standard temperature
- \(Q_{std}\) = equivalent standard volumetric flow
Typical Gas Properties for Choked Flow
Use gas-specific values when available. The values below are common approximations for ideal-gas calculations near room temperature.
| 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 0.0146 kg/s.
Example 2: Air with no downstream pressure entered
Suppose you enter these values:
- Upstream pressure: 10 bar(a)
- Temperature: 20°C
- Specific heat ratio: 1.40
- Molar mass: 28.97 g/mol
- Discharge coefficient: 0.98
- Orifice area: 10 mm²
With no downstream pressure entered, the calculation assumes the flow can become choked. The maximum choked mass flow is approximately 0.0233 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. A well-designed nozzle may have a value near 0.95 to 1.00. A sharp-edged orifice is often closer to 0.60 to 0.65. If you have measured or manufacturer-provided data, use that value instead of a generic estimate.
