BIZOMAT MAKEOS · Pneumatics
Compressed Air Leak Cost
How much air does this leak waste, and what does it cost each year?
Air lost through a leak hole by choked-flow theory (or a measured leak flow), the compressor power it uses and its yearly energy cost.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Equivalent hole diameter | mm | Diameter of a round hole with the same leakage (estimate from an ultrasonic survey). |
| Line pressure (gauge) | bar | Pressure in the line at the leak. |
| Discharge coefficient | Discharge coefficient of the leak path (about 0.6–0.8). | |
| Line air temperature | °C | Temperature of the air in the line. |
| Measured leak flow (0 = use hole) | L/s free air | Leak flow measured by a flow meter or leak-down test, in litres per second of free air; 0 to estimate from the hole. |
| Compressor specific power | kW per m³/min | Compressor package power per m³/min of free air delivery, from the compressor data sheet or an air audit (about 6–7 for many screw compressors at 7 bar). |
| Pressurised hours per year | h | Hours per year the system is under pressure. |
| Electricity price | AUD/kWh | Electricity price per kWh. |
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: Equivalent hole diameter
- What it is
- The diameter of a round hole that would leak the same amount of air as the actual leak, usually estimated during an ultrasonic leak survey.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Leak flow and cost rise with the square of hole diameter.
- Get it right
- Ignored if a measured leak flow is entered.
What this means: Line pressure (gauge)
- What it is
- The air pressure in the line at the point of the leak, read from a nearby gauge.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0.000001 bar to 100 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Higher pressure raises the estimated leak flow from a hole.
- Get it right
- Enter gauge pressure; the tool adds atmospheric pressure itself.
What this means: Discharge coefficient
- What it is
- The ratio of actual flow through the leak path to ideal flow through a sharp hole of the same size, allowing for the shape of the gap.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 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
- Estimated leak flow and cost rise in direct proportion.
- Get it right
- Enter a fraction below one. Ignored if a measured leak flow is entered.
What this means: Line air temperature
- What it is
- The temperature of the compressed air in the line at the leak.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -40 °C to 200 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Warmer air gives slightly less estimated leak flow.
- Get it right
- Use line temperature, not compressor discharge temperature.
What this means: Measured leak flow (0 = use hole)
- What it is
- The leak flow measured directly with a flow meter or leak-down test, expressed as free air. When entered, it replaces the hole estimate.
- Units and format
- Enter a number in L/s free air: L/s free air. The form accepts 0 L/s free air to 100000 L/s free air. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 L/s free air as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Cost rises in direct proportion.
- Get it right
- 0 means use the hole estimate. Enter litres per second of free air, not compressed air.
What this means: Compressor specific power
- What it is
- The electrical power the compressor package uses for each cubic metre per minute of free air it delivers, from its data sheet or an air audit.
- Units and format
- Enter a number in kW per m³/min: kW per m³/min. The form accepts 0.000001 kW per m³/min to 100 kW per m³/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6.5 kW per m³/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Power and cost rise in direct proportion.
- Get it right
- Use package input power including dryer and fan if they run with it.
What this means: Pressurised hours per year
- What it is
- The hours each year the air system is under pressure, which is when the leak runs.
- Units and format
- Enter a number in h: hours. The form accepts 0.000001 h to 8784 h. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6000 h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Yearly energy and cost rise in direct proportion.
- Get it right
- Count hours pressurised, including nights and weekends if the system stays on.
What this means: Electricity price
- What it is
- What you pay for one kilowatt-hour of electricity, from your bill or energy contract.
- Units and format
- Enter a number in AUD/kWh: Australian dollars per kilowatt-hour. The form accepts 0 AUD/kWh to 100 AUD/kWh. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.25 AUD/kWh as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Cost rises in direct proportion.
- Get it right
- Use the average tariff over the hours the system runs.
Method and formulas
- Choked mass flow ṁ = Cd A p₀ √(k ÷ (R T₀)) × (2 ÷ (k + 1))^((k + 1)/(2(k − 1))), with p₀ absolute, k = 1.4, R = 287 J/kg·K.
- Flow of free air = ṁ ÷ ρ_free (1.204 kg/m³ at 1.013 bar, 20 °C).
- Power = free air (m³/min) × specific power; cost = power × hours × price.
- Example: a 3 mm leak at 7 bar wastes 7.1573 L/s, about 2.7914 kW, costing $4,187 a year.
Limitations
- Choked flow applies when line pressure exceeds about 0.9 bar gauge; real leak paths vary widely.
- Compressor part-load behaviour may mean savings are lower than the average specific power suggests.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Prioritise leaks found in a leak survey
- Justify a leak repair programme
- Estimate savings from lowering line pressure
Who it is for
- Maintenance engineers
- Energy and utilities managers
- Design engineers
What you get
- Leak flow in free air
- Compressor power wasted
- Energy and cost per year
Interpreting the result
- Fix the largest leaks first; a leak survey usually pays back within months.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3032–3041. 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
Choosing a meter and the cost of error
In Flow Measurement by the Numbers
What it covers: A selection method across fluid, range, accuracy, pressure loss, installation and cost, sizing for the range, valuing a meter’s error, and appraising a meter that reveals compressed-air leaks.
Method explained here · BIZOMAT original book
Pneumatics by the Numbers
What it covers: Size a pneumatic cylinder, time and cushion its stroke, choose valves and a safe fail state, count air and leak costs, supply clean air and commission and maintain the system.
Method explained here · BIZOMAT original book
How gas flows through a leak
In Production Leak Testing by the Numbers
What it covers: Mean free path and Knudsen number, viscous, molecular and choked flow through leaks, how leak rate changes with pressure and gas, and converting a helium result to air correctly.
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