Compressor Power Calculator Formula
Understand the math behind the compressor power calculator. Each variable explained with a worked example.
Formulas Used
Ideal (Isentropic) Power
ideal_power = flow_rate * cp * inlet_temp * (pow(pressure_ratio, gm1_g) - 1)Actual Shaft Power
actual_power = flow_rate * cp * inlet_temp * (pow(pressure_ratio, gm1_g) - 1) / etaDischarge Temperature
outlet_temp = inlet_temp * (1 + (pow(pressure_ratio, gm1_g) - 1) / eta)Variables
| Variable | Description | Default |
|---|---|---|
flow_rate | Mass Flow Rate (m)(kg/s) | 1 |
inlet_temp | Inlet Temperature (T1)(K) | 300 |
pressure_ratio | Pressure Ratio (P2/P1) | 4 |
gamma | Specific Heat Ratio (gamma) | 1.4 |
cp | Specific Heat (Cp)(kJ/(kg·K)) | 1.005 |
efficiency | Isentropic Efficiency(%) | 80 |
gm1_g | Derived value= (gamma - 1) / gamma | calculated |
eta | Derived value= efficiency / 100 | calculated |
How It Works
Adiabatic Compressor Power
The isentropic (ideal adiabatic) compression process provides the theoretical minimum power needed. Real compressors require more power due to irreversibilities.
Formula
W_ideal = m × Cp × T1 × (PR^((gamma-1)/gamma) - 1)
W_actual = W_ideal / eta_isentropic
T2 = T1 × (1 + (PR^((gamma-1)/gamma) - 1) / eta)
where PR is the pressure ratio, gamma is the specific heat ratio, and eta is the isentropic efficiency.
Worked Example
Compressing 1 kg/s of air from 300 K with pressure ratio 4, gamma=1.4, eta=80%.
- 01(gamma-1)/gamma = 0.4/1.4 = 0.2857
- 02PR^0.2857 = 4^0.2857 = 1.486
- 03Ideal power = 1 × 1.005 × 300 × (1.486 - 1) = 301.5 × 0.486 = 146.5 kW
- 04Actual power = 146.5 / 0.80 = 183.2 kW
- 05T2 = 300 × (1 + 0.486/0.80) = 300 × 1.608 = 482.3 K
Frequently Asked Questions
What is typical isentropic efficiency?
Centrifugal compressors: 75-85%, axial compressors: 85-92%, reciprocating compressors: 70-85%, screw compressors: 70-80%. Larger, more advanced machines tend toward the higher end.
Why is discharge temperature important?
High discharge temperatures can damage seals and lubricants, cause thermal expansion issues, and limit the pressure ratio per stage. Air compressors are often limited to about 200°C discharge, requiring intercooling for high pressure ratios.
When is multi-stage compression needed?
For pressure ratios above about 3-4 per stage (depending on gas and machine type), intercooling between stages reduces power consumption and limits discharge temperature. The ideal approach uses equal pressure ratios per stage.
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