Calculated Results
Results appear here after submission and stay above the form.
Flow Curve
Mass flow is plotted against downstream pressure ratio. Choked flow forms a plateau after the critical pressure ratio is crossed.
Summary
Calculator Inputs
Use absolute pressures for compressible flow calculations. The form uses three columns on large screens, two on medium screens, and one on mobile.
Example Data Table
These values are illustrative engineering examples. Results assume one-dimensional compressible flow with the listed coefficients and gas properties.
| Gas | P0 (kPa abs) | P2 (kPa abs) | T0 (K) | Area (mm²) | Flow regime | ṁ (kg/s) | Critical ratio | T* / Te (K) |
|---|---|---|---|---|---|---|---|---|
| Air | 700 | 300 | 300 | 150 | Choked | 0.2401 | 0.5283 | 250.0 |
| Nitrogen | 900 | 500 | 315 | 120 | Subcritical | 0.2342 | 0.5283 | 266.3 |
| Helium | 600 | 200 | 295 | 80 | Choked | 0.0427 | 0.4881 | 221.8 |
| Carbon dioxide | 1200 | 800 | 320 | 200 | Subcritical | 0.5961 | 0.5477 | 292.2 |
Formula Used
1) Critical pressure ratio
r* = (2 / (γ + 1))^(γ / (γ - 1))
Flow becomes choked when P2 / P0 ≤ r*. At that point, lowering downstream pressure further no longer increases mass flow.
2) Choked mass flux
G* = Cd × P0 / √(ZRT0) × √γ × (2 / (γ + 1))^((γ + 1) / (2(γ - 1)))
Mass flow rate is ṁ = G × A. This is the controlling flow rate once sonic conditions exist at the minimum section.
3) Subcritical mass flux
G = Cd × P0 / √(ZRT0) × √[(2γ / (γ - 1)) × (r^(2/γ) - r^((γ + 1)/γ))]
Use this when r = P2 / P0 is above the critical ratio. Flow remains pressure-dependent in this regime.
4) Controlling temperature and pressure
T* = T0 × 2 / (γ + 1)
P* = P0 × r*
For subcritical operation, the exit temperature is Te = T0 × r^((γ - 1)/γ) and exit pressure is approximately P2.
5) Sonic velocity and density
a = √(γRT)
ρ = P / (ZRT)
These values help estimate volumetric flow, choking onset, and the controlling state at the throat or exit.
How to Use This Calculator
- Enter the upstream stagnation pressure, downstream pressure, and upstream temperature in consistent absolute units.
- Select a gas preset or manually enter
γ,R,Z, and the discharge coefficient. - Choose whether you want to enter direct flow area or diameter. The calculator converts geometry to square meters internally.
- Press the calculate button. The result block appears above the form and below the page header.
- Review the flow regime, critical pressure ratio, mass flux, mass flow rate, controlling temperature, pressure, density, and velocity.
- Use the chart to see how mass flow changes with downstream pressure ratio and where the choking plateau begins.
- Export the current result as CSV or PDF for reports, design checks, or engineering review notes.
FAQs
1) What is critical flow rate?
Critical flow rate is the maximum mass flow through a restriction when the local Mach number reaches one at the minimum area.
2) Why must pressures be absolute?
Compressible flow equations use absolute thermodynamic pressure. Gauge pressure can produce incorrect pressure ratios and wrong choking predictions.
3) What does the discharge coefficient represent?
It accounts for real losses, vena contracta effects, and nonideal nozzle or orifice behavior. Lower values reduce predicted mass flow.
4) When does flow become choked?
Flow becomes choked when the downstream-to-upstream pressure ratio falls to or below the critical ratio defined by the gas heat-capacity ratio.
5) Does lowering downstream pressure always increase flow?
No. Once choking starts, the controlling section is sonic. Further downstream pressure reduction does not increase mass flow through that section.
6) Can I use diameter instead of area?
Yes. Switch the geometry mode to diameter. The calculator converts it to flow area before computing mass flux and mass flow.
7) Why is compressibility factor included?
It adjusts gas density away from ideal behavior. For many moderate conditions, Z is near one, but it matters at higher pressures.
8) Is this suitable for liquids?
No. This page targets compressible gas flow. Liquid critical flow and cavitating flow need different correlations and property models.