KEVOS® MAKEOS · Engineering
Gas Compressor or Turbine Isentropic Efficiency from Measured Temperatures (Power, Entropy Generation)
From the measured inlet and outlet pressures and temperatures of an uncooled gas compressor, blower or turbine, what is its isentropic efficiency, shaft power and entropy generation, and does the efficiency meet the minimum you expect?
Isentropic efficiency of an uncooled gas compressor, blower, turbine or expander from measured inlet and outlet pressures and temperatures: the isentropic outlet temperature, the efficiency, the gas power absorbed or delivered, the ideal power, and the entropy change and generation rate, against the minimum efficiency you expect.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Machine | choice | Compressor or blower when the pressure rises; turbine or expander when it falls. |
| Measured inlet and outlet | ||
| Inlet pressure (absolute) | kPa | Absolute pressure at the inlet: gauge reading plus atmospheric pressure. |
| Inlet temperature | °C | Gas temperature at the inlet, measured in the flow close to the flange. |
| Outlet pressure (absolute) | kPa | Absolute pressure at the outlet: gauge reading plus atmospheric pressure. |
| Outlet temperature | °C | Gas temperature at the outlet, measured in the flow before any cooler. |
| Gas, flow and target | ||
| Specific heat of the gas at constant pressure | kJ/kg·K | Specific heat of the gas at constant pressure: 1.005 kJ/kg·K for air near room temperature. |
| Specific heat ratio of the gas (cp ÷ cv) | Ratio of specific heats of the gas: 1.4 for air and nitrogen. | |
| Gas mass flow | kg/s | Gas mass flow from a flow meter or the maker’s curve at the operating point. |
| Minimum acceptable isentropic efficiency | % | The lowest isentropic efficiency you accept, from the maker’s data, the commissioning test or your trend. |
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: Machine
- What it is
- Whether the machine raises the gas pressure (compressor or blower) or lets the gas expand to produce work (turbine or expander).
- Units and format
- Choose one of 2 options from the list: Compressor or blower (pressure rises); Turbine or expander (pressure falls).
- Example
- The form opens with “Compressor or blower (pressure rises)” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Switches the efficiency formula between the compressor and turbine forms.
- Get it right
- Pressures and temperatures must rise for a compressor and fall for a turbine, or the tool asks you to check them.
Measured inlet and outlet
What this means: Inlet pressure (absolute)
- What it is
- The absolute pressure of the gas entering the machine, at the inlet flange.
- Units and format
- Enter a number in kPa: kilopascals. The form accepts 1 kPa to 100000 kPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 kPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher inlet pressure lowers the pressure ratio and the isentropic temperature change.
- Get it right
- Add atmospheric pressure to a gauge reading; a 1 kPa error matters at low pressure ratios.
What this means: Inlet temperature
- What it is
- The temperature of the gas entering the machine, measured in the gas stream at the inlet.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -100 °C to 1500 °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.
- Effect on the result
- Sets the isentropic outlet temperature; small errors move the efficiency a lot at low pressure ratios.
- Get it right
- Shield the probe from sun and radiant heat; surface readings on the pipe are not good enough.
What this means: Outlet pressure (absolute)
- What it is
- The absolute pressure of the gas leaving the machine, at the outlet flange.
- Units and format
- Enter a number in kPa: kilopascals. The form accepts 1 kPa to 100000 kPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 400 kPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher outlet pressure raises the isentropic temperature change and, for a compressor, the efficiency.
- Get it right
- Measure before any valve or cooler; add atmospheric pressure to a gauge reading.
What this means: Outlet temperature
- What it is
- The temperature of the gas leaving the machine, measured in the gas stream before any aftercooler.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -150 °C to 1500 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 190 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- For a compressor a hotter outlet lowers the efficiency; for a turbine a colder outlet raises it.
- Get it right
- Readings taken after an aftercooler or on an oil-injected machine make the efficiency look too high.
Gas, flow and target
What this means: Specific heat of the gas at constant pressure
- What it is
- The energy needed to raise one kilogram of the gas by one kelvin at constant pressure, which turns the temperature change into power.
- Units and format
- Enter a number in kJ/kg·K: kilojoules per kilogram per kelvin. The form accepts 0.5 kJ/kg·K to 20 kJ/kg·K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.005 kJ/kg·K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Power scales in proportion; with k it also sets the gas constant used for entropy.
- Get it right
- Air is about 1.005 kJ/kg·K near room temperature; keep it consistent with k.
What this means: Specific heat ratio of the gas (cp ÷ cv)
- What it is
- The ratio of the specific heats of the gas, which sets the ideal temperature change for the measured pressure ratio.
- 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.
- Effect on the result
- A higher ratio raises the isentropic temperature change and, for a compressor, the efficiency.
- Get it right
- Use 1.4 for air and nitrogen, about 1.3 for carbon dioxide; check data for other gases.
What this means: Gas mass flow
- What it is
- The mass of gas passing through the machine each second, which turns the temperature change into power.
- Units and format
- Enter a number in kg/s: kg/s. The form accepts 0.0001 kg/s to 10000 kg/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 kg/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Powers and entropy generation rise in proportion; efficiency does not change.
- Get it right
- Use a measured flow where you can; the maker’s curve is only right at the curve’s speed and inlet conditions.
What this means: Minimum acceptable isentropic efficiency
- What it is
- The lowest isentropic efficiency you accept for this machine, such as the maker’s guarantee less an allowance, or a trend limit.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 1% 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
- Only moves the pass or fail line of the efficiency check.
- Get it right
- Set it from the commissioning result so later tests show decline.
Method and formulas
- Isentropic outlet temperature T₂ₛ = T₁ (P₂ ÷ P₁)^((k−1)/k), temperatures in kelvin and pressures absolute.
- Compressor η = (T₂ₛ − T₁) ÷ (T₂ − T₁); turbine η = (T₁ − T₂) ÷ (T₁ − T₂ₛ).
- Gas power = ṁ cp |T₂ − T₁|; ideal power = ṁ cp |T₂ₛ − T₁|.
- Entropy change Δs = cp ln(T₂ ÷ T₁) − R ln(P₂ ÷ P₁) with R = cp (k − 1) ÷ k; generation rate ṁ Δs, which must be positive in an adiabatic machine.
- Example: air compressed from 100 to 400 kPa absolute and from 20 to 190 °C has an isentropic outlet of 162.47 °C and an efficiency of 83.81 %, absorbing 85.425 kW at 0.5 kg/s: above a 75 % minimum.
Limitations
- Adiabatic machines only: oil-injected, water-jacketed or intercooled compressors lose heat, so their outlet temperature understates the work and the efficiency comes out too high.
- Ideal gas with constant specific heats; kinetic energy changes and heat loss from the casing are neglected. Temperature sensors must sit in the gas stream, not on the pipe surface.
- A field screening check, not an acceptance test; ISO 5389, ASME PTC 10 and ISO 1217 set the test procedures and corrections for contractual tests.
- Example values are illustrations. Replace them with readings from your actual machine.
Typical uses
- Check a blower, centrifugal compressor or turbine against its expected efficiency from site readings
- Track performance decline from fouling or wear between overhauls
- Catch faulty gauges or thermometers when the result exceeds 100 %
Who it is for
- Maintenance and reliability engineers
- Plant and commissioning engineers
- Rotating-equipment technicians
What you get
- Isentropic efficiency and outlet temperature
- Gas power absorbed or delivered and the ideal power
- Pressure ratio
- Entropy change and generation rate
- Efficiency against the minimum
Interpreting the result
- A falling efficiency at the same pressure ratio and flow usually points to fouling, wear or internal leakage; compare at the same operating point.
- An efficiency above 100 % is impossible: it means heat is being removed or a reading is wrong.
Before relying on the result
- Check gauges and thermometers for calibration and position before acting on a low result.
- Compare with the maker’s performance curve at the measured flow and speed.
References
- Çengel Y. A. and Boles M. A., Thermodynamics: An Engineering Approach, 5th edition (McGraw-Hill, 2006), chapter 7 (sections 7-9 and 7-12: entropy change and isentropic processes of ideal gases, isentropic efficiencies of turbines and compressors). Method reference; no tables, figures or examples are reproduced.
- ISO 5389 Turbocompressors: performance test code; ASME PTC 10 Axial and Centrifugal Compressors and Exhausters; ISO 1217 Displacement compressors: acceptance tests (named by number and scope only).
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Explains the concept · KEVOS® original book
Compression and expansion
What it covers: The minimum work to compress air, isothermal and isentropic benchmarks, why intercooling helps, what heat of compression is worth, and why air tools cost far more energy than electric ones.
Also in Calculating entropy changes
Method explained here · KEVOS® original book
Compressors and turbines in steady flow
In On-Site Power and Heat by the Numbers
What it covers: The steady-flow energy equation for compressors, turbines, nozzles and throttles, isentropic efficiency from measured temperatures, and a turbocharger test that checks its own power balance.
Useful alongside · KEVOS® 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.
KEVOS® 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.