Calculator Inputs
Enter consistent operating data. Press calculate to check whether the restriction reaches sonic choking conditions.
Flow Curve
The graph plots normalized downstream pressure ratio against estimated mass flow. The plateau marks the choked region where more backpressure reduction no longer increases flow.
Formula Used
This calculator applies an ideal-gas compressible flow check with discharge coefficient and compressibility factor corrections. Upstream pressure and temperature must be absolute values.
Critical pressure ratio
(P* / P₁) = (2 / (γ + 1))^(γ / (γ - 1))
Choked condition
Flow is choked when P₂ / P₁ ≤ (P* / P₁)
Choked mass flow rate
ṁ = Cd × A × P₁ × √[γ / (Z × R × T₁)] × (2 / (γ + 1))^((γ + 1) / (2(γ - 1)))
Subcritical mass flow rate
ṁ = Cd × A × P₁ × √[(2γ / (ZRT₁(γ - 1))) × ((P₂/P₁)^(2/γ) - (P₂/P₁)^((γ + 1)/γ))]
Inlet density and volumetric flow
ρ₁ = P₁ / (ZRT₁), Q₁ = ṁ / ρ₁
These equations are widely used for nozzle, valve, and restriction screening. Real equipment may require vendor coefficients, expansion factors, and non-isentropic corrections.
How to Use This Calculator
- Enter the gas label for reporting clarity.
- Provide upstream and downstream absolute pressures in the same unit system.
- Enter upstream temperature and select its unit.
- Set γ, the specific gas constant, compressibility factor, and discharge coefficient.
- Enter the throat or restriction area and select its area unit.
- Click Calculate to display the result above the form.
- Review choking status, critical ratio, mass flow, and chart behavior.
- Use CSV or PDF export when sharing design checks or records.
Example Data Table
| Case | Gas | P₁ | P₂ | T₁ | γ | Area | Status | Mass Flow |
|---|---|---|---|---|---|---|---|---|
| 1 | Air | 6.0 bar(a) | 2.8 bar(a) | 25 °C | 1.40 | 250 mm² | Choked | 0.341 kg/s |
| 2 | Nitrogen | 4.0 bar(a) | 3.0 bar(a) | 30 °C | 1.40 | 180 mm² | Subcritical | 0.143 kg/s |
| 3 | Helium | 8.0 bar(a) | 3.5 bar(a) | 20 °C | 1.66 | 95 mm² | Choked | 0.069 kg/s |
Frequently Asked Questions
1. What does choked flow mean?
Choked flow means the gas reaches sonic velocity at the restriction throat. Lowering downstream pressure further does not increase mass flow unless upstream conditions or effective flow area also increase.
2. Why must pressure be absolute?
Compressible flow equations depend on the true thermodynamic pressure level. Gauge pressure omits atmospheric pressure and can misclassify the choking threshold or produce incorrect mass-flow results.
3. What value should I use for γ?
Use the ratio of specific heats for your gas near the operating temperature. Air is commonly approximated as 1.4, while other gases can vary significantly with composition and temperature.
4. What does the discharge coefficient represent?
The discharge coefficient adjusts ideal flow to better match real losses through a nozzle, orifice, or valve. A lower value reduces predicted mass flow for the same pressure conditions.
5. Does this calculator work for liquids?
No. This page is intended for gas-phase compressible flow screening. Liquids need different cavitation, flashing, and incompressible-flow methods that are not covered by these equations.
6. What is the compressibility factor used for?
The Z factor corrects ideal-gas density behavior. Use 1.0 for ideal or near-ideal conditions. For higher pressures or nonideal gases, enter a more representative value.
7. Why does the graph flatten in the choked region?
Once the throat reaches Mach 1, the mass flow becomes limited by upstream stagnation conditions and throat area. Additional downstream pressure reduction no longer raises flow.
8. Is this calculator suitable for final equipment sizing?
It is best for fast engineering checks and concept screening. Final sizing should consider valve data, installation effects, standards, safety factors, and vendor-specific performance coefficients.