BIZOMAT 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). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Tank pressure (gauge)
- What it is
- The pressure of the air inside the tank or line as read on a gauge, above atmospheric. The tool adds standard atmospheric pressure to get the absolute value.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0.000001 bar to 1000 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Once the flow is choked, mass flow rises in proportion to the absolute tank pressure while the velocity stays sonic.
- Get it right
- Gauge pressure: do not add atmospheric pressure yourself. 1 bar = 100 kPa.
What this means: Outside pressure (absolute)
- What it is
- The absolute pressure of the space the air escapes into, usually the local atmosphere; with the tank pressure it sets the ratio that decides whether the flow chokes.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0.000001 bar to 1000 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.01325 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Absolute, not gauge: the standard atmosphere is 1.01325 bar, and local pressure is lower at altitude.
What this means: Air temperature in the tank
- What it is
- The temperature of the compressed air inside the tank, upstream of the orifice; it is converted to kelvin for the velocity and flow equations.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -50 °C to 500 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 21 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The escape velocity rises with the square root of the absolute temperature.
What this means: Ratio of specific heats
- What it is
- The ratio of the gas’s specific heat at constant pressure to its specific heat at constant volume (cp ÷ cv), which governs how it cools as it expands.
- Units and format
- Enter a plain number with no unit. The form accepts 1.01 to 1.7. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.4 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from gas property tables for the gas actually being released.
What this means: Orifice diameter
- What it is
- The diameter of the hole, leak or nozzle the air escapes through, at its narrowest point.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Mass flow and free-air flow rise with the square of the diameter; the velocity does not change.
What this means: Discharge coefficient
- What it is
- The ratio of the actual flow through the orifice to the ideal flow, allowing for contraction of the jet and friction at the edge; it depends on the orifice shape.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.65 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Mass flow and free-air flow rise in proportion.
- Get it right
- It reduces the flow only, not the velocity; take it from orifice test data or a flow handbook for your hole shape.
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.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Set the pressure and stop the waste
In Compressed Air Plant by the Numbers
What it covers: Price each 100 kPa of CA-1's pressure, see how leaks and open blow-offs grow with it, find the pressure lost before the air leaves the room, and fix a low-pressure complaint at its cause.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
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