BIZOMAT MAKEOS · Pneumatics
Air Compressor Staging Check (Power and Discharge Temperature)
Should this air compressor be single- or two-stage: how much power does each take, what discharge temperature does each reach, and does the chosen arrangement stay within the temperature limit?
Comparison of single-stage and two-stage compression with perfect intercooling: pressure ratio, adiabatic and shaft power for one and two stages (as the compressor power tool), the best intermediate pressure √(p₁ p₂), the ideal adiabatic discharge temperature for each case (as the gas compression process tool) and the actual temperature allowing for the adiabatic efficiency, the power saved by staging, and the discharge temperature of the chosen arrangement against your limit.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Air delivery (as free air) | m³/min | Air delivered, as free air at inlet conditions. |
| Inlet pressure (absolute) | bar | Absolute pressure at the inlet. |
| Discharge pressure (gauge) | bar | Gauge pressure at discharge. |
| Inlet temperature | °C | Air temperature at the inlet (and after the intercooler). |
| Ratio of specific heats | Ratio of specific heats (1.4 for air). | |
| Adiabatic (overall) efficiency | % | Adiabatic efficiency used to turn ideal power and temperature rise into actual values. |
| Arrangement to check | choice | Arrangement whose discharge temperature is checked. |
| Largest discharge temperature | °C | Highest discharge temperature for the lubricant, valves and piping (your value from the maker). |
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: Air delivery (as free air)
- What it is
- The air the compressor delivers, expressed as free air at inlet conditions.
- Units and format
- Enter a number in m³/min: cubic metres per minute. The form accepts 0.000001 m³/min to 100000 m³/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 m³/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Shaft power rises in direct proportion.
- Get it right
- Use free air delivery, not the compressed volume at discharge pressure.
What this means: Inlet pressure (absolute)
- What it is
- The absolute pressure of the air at the compressor inlet.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0.1 bar to 50 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.013 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Absolute pressure: standard atmosphere is 1.01325 bar, not zero.
What this means: Discharge pressure (gauge)
- What it is
- The pressure the compressor delivers, as read on a gauge at the discharge.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0.000001 bar to 400 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.
- Get it right
- Gauge pressure; the tool adds standard atmosphere to get absolute.
What this means: Inlet temperature
- What it is
- The air temperature entering the first stage. The tool assumes the intercooler returns the air to this same temperature.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -40 °C to 80 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Ratio of specific heats
- What it is
- The ratio of specific heats, cp ÷ cv, of the gas being compressed.
- Units and format
- Enter a plain number with no unit. The form accepts 1.05 to 1.67. 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.
What this means: Adiabatic (overall) efficiency
- What it is
- The adiabatic efficiency: ideal compression power divided by actual shaft power. The tool also uses it to scale up the temperature rise.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 30% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 75% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A lower efficiency raises shaft power and discharge temperature.
What this means: Arrangement to check
- What it is
- The arrangement whose discharge temperature is checked against the limit and whose shaft power is reported as the main result.
- Units and format
- Choose one of 2 options from the list: Two-stage with intercooling; Single-stage.
- Example
- The form opens with “Two-stage with intercooling” selected as a worked example. Choose the option that matches your case.
What this means: Largest discharge temperature
- What it is
- The highest discharge temperature the lubricant, valves and pipework can accept, from the compressor maker.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts 0.000001 °C to 400 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 180 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- r = p₂(abs) ÷ p₁; adiabatic power = s k ÷ (k − 1) p₁ Q [r^((k−1)/(s k)) − 1] for s stages; shaft = adiabatic ÷ efficiency (as the compressor power tool).
- Best intermediate pressure p_i = √(p₁ p₂) (equal ratio per stage, intercooled to inlet temperature).
- Ideal discharge T = T₁ r_s^((k−1)/k) (as the gas compression process tool); actual T = T₁ + (ideal rise) ÷ efficiency.
- Example: one stage needs 63.475 kW and reaches 334.89 °C; two stages need 54.165 kW and reach 154.36 °C, saving 14.666%.
Limitations
- Perfect intercooling to inlet temperature; real intercoolers leave a temperature approach.
- Ideal-gas, steady-flow model; oil-flooded screw compressors control discharge temperature by injection.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Choose between single- and two-stage compressors
- Check discharge temperature for oil and valve life
- Estimate the power saved by an intercooler
Who it is for
- Plant engineers
- Energy managers
- Maintenance engineers
What you get
- Pressure ratio and best intermediate pressure
- Power for one and two stages and the saving
- Discharge temperatures and the check
Interpreting the result
- Above a pressure ratio of about 4–5 per stage, discharge temperatures rise fast: staging protects valves and oil as well as saving power.
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
Discharge temperature, staging and cooling
In Compressed Air Plant by the Numbers
What it covers: Calculate how hot air gets in one isentropic stage, why oil injection and intercooled stages help, why an oil-flooded screw must stay above its own dew point, and what the aftercooler removes.
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Open the Air Compressor Staging Check (Power and Discharge Temperature) calculator