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%.
flow_rate = 1inlet_temp = 300pressure_ratio = 4gamma = 1.4cp = 1.005efficiency = 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
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