Enter the upstream absolute pressure, gas temperature, gas properties, discharge coefficient, and orifice area into the calculator to estimate the maximum choked (sonic) flow of an ideal gas through an orifice/nozzle. Choked flow is the limiting condition where the gas reaches Mach 1 at the minimum flow area, and further lowering downstream pressure does not increase the mass flow rate. (If you only have gauge pressure, add atmospheric pressure to convert to absolute pressure.)

Choked Flow Calculator (Ideal Gas)

Enter the upstream conditions and geometry, then click Calculate. Downstream pressure is optional (used only to check whether choking occurs).

Choose mass-flow units (kg/s, lbm/s) or standard volumetric units (SCFM at 1 atm & 60°F; SLPM and Nm³/h at 1 atm & 0°C).

Choked Flow Formula

For an ideal gas flowing through an orifice/nozzle, the maximum choked (sonic) mass flow rate is:

\dot{m} = C_d A P_1 \sqrt{\frac{k}{R T_1}\left(\frac{2}{k+1}\right)^{\frac{k+1}{k-1}}}

Choking occurs when the downstream-to-upstream absolute pressure ratio is at or below the critical value:

\frac{P_2}{P_1} \le \left(\frac{2}{k+1}\right)^{\frac{k}{k-1}}

Variables:

  • \(\dot{m}\) is the choked mass flow rate (e.g., kg/s)
  • \(C_d\) is the discharge coefficient (dimensionless)
  • \(A\) is the minimum flow area (m²)
  • \(P_1\) is the upstream absolute pressure (Pa, psia, etc.)
  • \(P_2\) is the downstream absolute pressure
  • \(T_1\) is the upstream absolute temperature (K)
  • \(k\) (also written \(\gamma\)) is the specific heat ratio \(c_p/c_v\) (dimensionless)
  • \(R\) is the specific gas constant (J/(kg·K)), where \(R = R_u/M\)

Once the flow is choked, the mass flow rate is limited by upstream conditions and the restriction geometry; lowering the downstream pressure further does not increase \(\dot{m}\).

What is Choked Flow?

Choked flow is a phenomenon in compressible flow where the fluid velocity reaches the speed of sound (Mach 1) at the minimum flow area (the “throat”/vena contracta). When this happens, the flow rate becomes limited by upstream conditions. Choking is determined by a critical downstream-to-upstream absolute pressure ratio that depends on the gas specific heat ratio \(k\). For example, for air with \(k \approx 1.4\), the critical ratio is about 0.528 (meaning choking begins when \(P_2 \lesssim 0.528\,P_1\), using absolute pressures).

How to Calculate Choked Flow?

The following steps outline how to calculate the choked (sonic) flow for an ideal gas through an orifice/nozzle.

  1. Determine the upstream absolute pressure \(P_1\).
  2. Determine the upstream temperature \(T_1\) (convert to Kelvin for calculation).
  3. Determine gas properties: specific heat ratio \(k\) and molar mass \(M\) (to compute \(R\)).
  4. Determine the restriction geometry: minimum flow area \(A\) and discharge coefficient \(C_d\).
  5. (Optional) Check the choking condition using downstream absolute pressure \(P_2\): choking occurs when \(\tfrac{P_2}{P_1} \le \left(\tfrac{2}{k+1}\right)^{\tfrac{k}{k-1}}\).
  6. Compute the maximum choked mass flow \(\dot{m}\) using the formula above.
  7. Convert \(\dot{m}\) to the desired mass-flow or standard volumetric units as needed (the calculator above performs these conversions).

Example Problem:

Use the following variables as an example problem to test your knowledge (air, ideal-gas assumption):

Upstream pressure (P1) = 100 psia

Downstream pressure (P2) = 40 psia (optional check)

Temperature (T1) = 60°F

Specific heat ratio (k) = 1.4

Molar mass (M) = 28.97 g/mol

Discharge coefficient (Cd) = 0.98

Orifice area (A) = 0.10 in²

Result (maximum choked flow): \(\dot{m} \approx 0.103\) kg/s (about 0.227 lbm/s), which is approximately 179 SCFM at 1 atm and 60°F.