Calculate choked mass flow rate, throat area, stagnation pressure, temperature, gas constant, or gamma from five known flow values.

Choked Mass Flow Rate Calculator

Enter any 5 values to calculate the missing variable









Related Calculators

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.

C_γ = √(γ)((2) / (γ + 1))⁽(γ + 1) / (2(γ - 1)))
m = (P₀ Aₜ C_γ) / (√(R T₀))
Aₜ = (m√(R T₀)) / (P₀ C_γ)
P₀ = (m√(R T₀)) / (Aₜ C_γ)
T₀ = (((P₀ Aₜ C_γ) / (m))²) / (R)
R = (((P₀ Aₜ C_γ) / (m))²) / (T₀)
C_γ = (m√(R T₀)) / (P₀ Aₜ)
  • ṁ = choked mass flow rate
  • At = throat area
  • P0 = 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 because gamma appears in both the base and exponent.

Typical Gas Constants and Gamma Values

Gas Specific Gas Constant R, J/(kg·K) 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 m², stagnation pressure of 500,000 Pa, stagnation temperature of 300 K, R = 287.05 J/(kg·K), and γ = 1.4.

For γ = 1.4, the choking coefficient is approximately 0.6847.

m = (500000(0.002)(0.6847)) / (√(287.05(300))) = 2.334 kg / s

The choked mass flow rate is approximately 2.334 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/(kg·K), and γ = 1.4.

Aₜ = (1.5√(287.05(290))) / (400000(0.6847)) = 0.00158 m²

The required throat area is approximately 0.00158 m².

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.