Calculator inputs
Velocity trend chart
This Plotly chart shows how velocity changes as downstream pressure ratio changes for the current temperature and gas settings.
Example data table
Use this example to verify layout, expected units, and output scale before entering live design conditions.
| Upstream Gauge (bar) | Downstream Abs (bar) | Temp (°C) | γ | R (J/kg·K) | Cd | Diameter (mm) | Flow State | Velocity (m/s) | Exit Temp (°C) | Flow Rate (m³/s) |
|---|---|---|---|---|---|---|---|---|---|---|
| 6.00 | 1.013 | 25.0 | 1.40 | 287.05 | 0.98 | 12.0 | Choked | 309.668 | -24.692 | 0.03502 |
Formula used
The calculator assumes steady, adiabatic, one-dimensional ideal-gas discharge from a reservoir through a nozzle or orifice.
P1,abs = Pgauge + Patm
r = P2 / P1rcrit = (2 / (γ + 1))γ / (γ - 1)
v = Cd × √[(2γ / (γ - 1)) × R × T1 × (1 - r(γ - 1)/γ)]
v = Cd × √[(2γ / (γ + 1)) × R × T1]
T2 = T1 × r(γ - 1)/γ for subsonic flowT2 = T1 × 2 / (γ + 1) for choked flow
A = πd² / 4Q = A × vṁ = ρ × Q
These equations are useful for quick engineering estimates. Real systems may also need friction, humidity, valve losses, and non-ideal nozzle geometry checks.
How to use this calculator
- Enter the upstream gauge pressure of the compressed air source.
- Enter downstream absolute pressure, usually the receiving pressure or local ambient value.
- Type the upstream air temperature in degrees Celsius.
- Keep γ at 1.4 and R at 287.05 for standard dry air unless you are modeling another gas.
- Enter a realistic discharge coefficient for the nozzle or opening.
- Enter the nozzle diameter in millimeters.
- Press Calculate Velocity to display results above the form.
- Review the chart, export the result table, and compare with the example row.
FAQs
1) What does choked flow mean here?
Choked flow means the pressure ratio falls below the critical value. Velocity reaches its maximum ideal nozzle condition for the given upstream temperature and gas properties, so lowering downstream pressure further will not raise velocity through the throat.
2) Why do I need downstream absolute pressure instead of gauge pressure?
Compressible-flow equations use absolute pressure because gas density depends on pressure measured from a perfect vacuum. If you only know downstream gauge pressure, add local atmospheric pressure first before entering the value.
3) What discharge coefficient should I use?
Use a value based on the nozzle, valve, or orifice shape. Sharp-edged openings often need lower values than smooth nozzles. If no test data exists, start with an engineering estimate and confirm it experimentally.
4) Is this calculator valid for long pipes?
Not by itself. This tool estimates discharge velocity at an opening or short nozzle. Long pipelines need extra pressure-loss calculations for friction, fittings, roughness, heat transfer, and sometimes unsteady behavior.
5) Why does the exit temperature drop?
When compressed air expands, internal energy converts into kinetic energy. Under adiabatic assumptions, that energy change lowers static temperature. The effect becomes more noticeable when the pressure ratio is large.
6) Can I use this for gases other than air?
Yes. Replace γ and R with values for the gas you are modeling, then review whether ideal-gas and adiabatic assumptions are still acceptable. Some gases may also require different discharge coefficients and safety checks.
7) What does Reynolds number add to the result?
It gives a quick sense of the discharge flow regime and helps with follow-up design work. High Reynolds numbers usually indicate inertia-dominated flow, which can influence loss coefficients, noise, and measurement approach.
8) Why is the velocity not always equal to the speed of sound?
The calculator multiplies ideal velocity by the discharge coefficient. That accounts for real losses, so even choked cases can show a value slightly below the local sonic speed for a perfect nozzle.