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Compressible Gas Nozzle Choked Flow & Sonic Discharge Calculator

Choked flow is a compressible fluid dynamics phenomenon where fluid velocity in a converging nozzle reaches sonic velocity (Mach 1.0) at the throat.

Absolute upstream reservoir pressure.

Reservoir absolute temperature (293.15 K = 20 °C).

Absolute pressure of the receiver or atmosphere.

Nozzle minimum throat cross-sectional area.

Adiabatic index (air = 1.40, steam = 1.33, helium = 1.66).

Calculated Result
0.0708 kg/s

Discharge Mass Flow Rate

Mass Flow Rate (ṁ)

0.0708 kg/s (254.93 kg/h)

Flow Regime

CHOKED (Sonic Mach 1.0 at Throat)

Critical Pressure Ratio (P*/P₀)

0.5283

Actual Pressure Ratio (Pb/P₀)

0.1688

Throat Sonic Velocity

313.3 m/s

Calculation Breakdown

  1. Critical Pressure Ratio Threshold(P*/P₀) = [2 / (1.4 + 1)]^(1.4/(1.4-1)) = 0.5283
  2. Choking Condition AssessmentActual Ratio = 1.013 / 6 = 0.1688 ≤ 0.5283 → Flow is CHOKED (Sonic)
  3. Choked Mass Flow Rate Formulationṁ = A_t × P₀ × √(γ / (R × T₀)) × [2/(γ+1)]^((γ+1)/(2(γ-1))) = 0.0708 kg/s

Compressible Nozzle Flow Parameters

Interactive visualization based on your current inputs

Value
0.07.8162331Critical RatioActual RatioMass Flow (kg/h / 10)Throat Speed (m/s / 10)ParameterValue

What Is the Compressible Gas Nozzle Choked Flow & Sonic Discharge Calculator?

Compressible gas nozzle flow describes the velocity and mass flow behavior of gases expanding through convergent or convergent-divergent nozzles.

How Does the Compressible Gas Nozzle Choked Flow & Sonic Discharge Calculator Work?

The critical pressure ratio P*/P0 is calculated from γ. If Pb/P0 ≤ P*/P0, sonic choked flow occurs and mass flow rate depends exclusively on upstream stagnation conditions.

Compressible Gas Nozzle Choked Flow & Sonic Discharge Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

\frac{P^*}{P_0} = \left( \frac{2}{\gamma + 1} \right)^{\frac{\gamma}{\gamma - 1}}, \quad \dot{m} = A_t P_0 \sqrt{\frac{\gamma}{R T_0}} \left( \frac{2}{\gamma + 1} \right)^{\frac{\gamma + 1}{2(\gamma - 1)}}

Compressible gas critical pressure ratio dictates sonic choking condition at nozzle throat. Choked mass flow scales directly with reservoir stagnation pressure and throat area.

How to Use the Compressible Gas Nozzle Choked Flow & Sonic Discharge Calculator

  1. Enter upstream absolute stagnation pressure and temperature.
  2. Provide downstream receiver back pressure.
  3. Enter nozzle throat area in mm² and gas γ ratio.

Step-by-Step Example Calculation

Compressed Air Tank Discharging to Atmosphere

Input Values:

stagnationPressureBar:6.0
stagnationTempKelvin:293.15
backPressureBar:1.013
throatAreaMm2:50.0
gasSpecificHeatRatio:1.40
Worked Steps: Flow is choked (actual ratio 0.169 ≤ 0.528 critical ratio), discharging 0.069 kg/s (248 kg/h) at 313 m/s sonic throat velocity.

Understanding Your Result

Flow Regime: Sonic Choked or Subsonic Unchoked.

Mass Flow Rate: Discharge mass in kg/s and kg/h.

Throat Velocity: Gas speed at the minimum cross-section.

Factors That Affect the Result

  • Higher upstream pressure directly scales choked mass flow; lower gas temperature increases fluid density and mass flow rate.

When Should You Use This Calculator?

  • Safety relief valve (PRV) sizing, rocket nozzle throat design, and industrial compressed air orifice blowdown.

Assumptions & Limitations

  • Assumes isentropic ideal gas expansion without boundary layer friction or shocks before the throat.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard gas dynamics isentropic compressible flow formulation.

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