KEVOS® MAKEOS · Pneumatics
Velocity and Flow of Escaping Compressed Air
How fast and how much air escapes from this tank through a hole or nozzle?
Theoretical velocity of air escaping adiabatically from a large container by the handbook formula, the velocity actually reached at a plain orifice (limited to sonic when the flow chokes), and the mass and free-air flow through an orifice of given size.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Tank pressure (gauge) | bar | Gauge pressure in the container. |
| Outside pressure (absolute) | bar | Absolute pressure outside the orifice (atmospheric is 1.01325 bar). |
| Air temperature in the tank | °C | Air temperature in the container. |
| Ratio of specific heats | Ratio of specific heats: 1.4 for air (the handbook uses 1.41). | |
| Orifice diameter | mm | Diameter of the hole or nozzle. |
| Discharge coefficient | Discharge coefficient of the orifice (sharp-edged about 0.6–0.65, rounded nozzle up to about 0.97; confirm for yours). |
Method and formulas
- Handbook (adiabatic): v₂ = √{2 k ÷ (k − 1) × R T × [1 − (p₂ ÷ p₁)^((k−1)/k)]}, with R = 287 J/kg·K.
- When p₂ ÷ p₁ is below (2 ÷ (k + 1))^(k/(k−1)) ≈ 0.53 the orifice flow chokes and the velocity there is sonic: √(2 k R T ÷ (k + 1)).
- Mass flow through the orifice uses the compressible orifice equations; free-air flow at 1.01325 bar and 20 °C.
- Example: air at 6 bar gauge through a 2 mm hole escapes at 313.86 m/s and 168.16 L/min of free air.
Limitations
- Large container, steady flow, ideal gas.
- Higher pressure does not raise the orifice velocity once choked; it raises the mass flow.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Estimate air loss through a leak or blow-off nozzle
- Check whether a vent is choked
- Size an orifice for a purge flow
Who it is for
- Compressed-air engineers
- Maintenance engineers
- Process engineers
What you get
- Escape velocity
- Whether the flow is choked
- Mass and free-air flow
Interpreting the result
- Use the free-air flow with the compressor’s specific power to price a leak.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3037–3038. Topic reference; no source tables or recommended settings are reproduced.
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