Select mass flow rate, throat area, stagnation pressure, temperature, gas constant, or gamma to solve from the other five values. This ideal sonic-throat model uses absolute stagnation pressure; an optional downstream pressure checks the choking condition.
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Choked Mass Flow Rate Formula
The choked mass flow rate equation used here is for ideal gas flow through a throat or nozzle when the flow reaches Mach 1 at the minimum area.
- ṁ = choked mass flow rate
- At = throat area
- P0 = absolute stagnation pressure, also called total pressure
- T0 = stagnation temperature, also called total temperature
- R = specific gas constant
- γ = ratio of specific heats, also called gamma or heat capacity ratio
- Cγ = choking coefficient based on gamma
To calculate mass flow rate, the equation multiplies stagnation pressure, throat area, and the choking coefficient, then divides by the square root of specific gas constant times stagnation temperature.
To calculate throat area, stagnation pressure, stagnation temperature, or specific gas constant, the same equation is rearranged algebraically. To calculate gamma, the calculator solves the choking coefficient equation numerically over 1.00000001โ5 because gamma appears in both the base and exponent. Values outside this range are rejected; constant gas properties and ideal flow with discharge coefficient 1 are assumed.
Typical Gas Constants and Gamma Values
| Gas | Specific Gas Constant R, J/(kgยทK) | Typical Gamma γ |
|---|---|---|
| Air | 287.05 | 1.40 |
| Nitrogen | 296.8 | 1.40 |
| Oxygen | 259.8 | 1.40 |
| Carbon dioxide | 188.9 | 1.29 to 1.30 |
| Helium | 2077 | 1.66 |
| Hydrogen | 4124 | 1.41 |
Choked Flow Pressure Ratio Check
Choked flow occurs only when the downstream pressure is low enough compared with the stagnation pressure. A common ideal-gas check is the critical pressure ratio shown below.
| Gamma γ | Critical Static-to-Stagnation Pressure Ratio | Meaning |
|---|---|---|
| 1.30 | 0.546 | Downstream pressure must be about 54.6% of P0 or lower |
| 1.40 | 0.528 | Common air value |
| 1.66 | 0.488 | Typical monatomic gas value |
Example Problems
Example 1: Calculate choked mass flow rate for air
Suppose air has a throat area of 0.002 mยฒ, stagnation pressure of 500,000 Pa, stagnation temperature of 300 K, R = 287.05 J/(kgยทK), and γ = 1.4.
For γ = 1.4, the choking coefficient is approximately 0.6847.
The choked mass flow rate is approximately 2.333 kg/s.
Example 2: Calculate required throat area
You need a choked mass flow rate of 1.5 kg/s for air with P0 = 400,000 Pa, T0 = 290 K, R = 287.05 J/(kgยทK), and γ = 1.4.
The required throat area is approximately 0.00158 mยฒ.
FAQ
What does choked flow mean?
Choked flow means the gas velocity reaches Mach 1 at the throat. Once this happens, lowering the downstream pressure further does not increase the mass flow rate for the same upstream stagnation pressure and temperature.
Should stagnation pressure and temperature be used instead of static values?
Yes. This equation uses stagnation pressure P0 and stagnation temperature T0. Static pressure and static temperature at some other point in the flow are not the same inputs unless they are specifically equal to the stagnation values for your case.
Why must gamma be greater than 1?
Gamma is the ratio of specific heats, Cp/Cv, for a gas. For ideal gases used in this equation, gamma is greater than 1. Values at or below 1 make the choking coefficient invalid.
