Air compressor efficiency calculation formula

The efficiency calculation of air compressor involves multiple parameters and formulas, the following is a detailed description for you:

1. core calculation formula

the total efficiency (& eta;_total) of the air compressor is calculated by the ratio of theoretical power to shaft power, and is divided into isothermal efficiency and adiabatic efficiency:

• isothermal total efficiency:

ηtotal,isothermal =Pshaft Pisothermal

• adiabatic total efficiency:

ηtotal,adiabatic =Pshaft Padiabatic

key parameter analysis

1. theoretical power

   • isothermal theoretical power (P_isothermal): The theoretical required power when the compression process is assumed to be completely isothermal.

Pisothermal =Q⋅R⋅Tln ⋅ln(Pinlet Pdischarge)

	- $ Q $: displacement (m & sup3;/min)
	- $ R $: gas constant (287 J/(kg · K) for air)
	- $ T_{ text{ln}} $: logarithmic mean temperature (K),$ T_{ text{ln}} = frac{T_{ text{inlet}} + T_{ text{discharge }}}{ 2} $
	- $ P_{text{discharge}} $/$ P_{text{inlet}} $: Exhaust/inlet pressure (absolute, MPa)

• adiabatic theoretical power (P_adiabatic): The theoretical required power when the compression process is assumed to be fully adiabatic.

Padiabatic =κ−1Q⋅κ ⋅R⋅Tinlet ⋅[(Pinlet Pdischarge )κκ−1 −1]

- $ kappa $: adiabatic index (1.4 for air)

2. Shaft power (P_shaft)
motor efficiency and transmission efficiency are considered through motor input power calculation:

Pshaft =ηmotor ⋅ηtransmission Pelectrical

• pelectrical: motor input power (kW)
• & eta;motor: motor efficiency (typical value 90%-95%)
• & eta;transmission: transmission efficiency (1 for direct connection, about 0.98 for belt transmission)

3. & eta;_mechanical
   efficiency reflecting internal friction and leakage losses:

& eta;mechanical = Pshaft Pisothermal or & eta;mechanical = Pshaft Padiabatic

2. Calculation Example

take an air compressor as an example:

• parameters:
  • displacement Q = 20m 3/min
  • exhaust pressure Pdischarge = 0.7MPa
  • inlet pressure Pinlet = 0.1MPa
  • inlet temperature Tinlet = 293K(20 ℃)
  • motor input power Pelectrical = 18kW
  • motor efficiency & eta;motor = 0.95, transmission efficiency & eta;transmission = 0.98
• calculation steps:

  1. shaft power:

Pshaft =0.95×0.9818 ≈19.3kW

2. isothermal theoretical power:

Tln =2293+(293×0.7/0.1) =366K
Pisothermal =20×287×366×ln(7)≈14.5kW

3. adiabatic theoretical power:

Padiabatic =0.420×1.4 ×287×293×(70.286−1)≈17.2kW

4. total efficiency:
   • isothermal efficiency: & eta;total,isothermal = 14.5/19.3 & asymp;75%
   • adiabatic efficiency: & eta;total,adiabatic = 17.2/19.3 & asymp;89%

3. simplified estimation method

use specific power (kW/m & sup3;/min) quickly assess efficiency:

specific Power = QPshaft

• example: If the specific power is 0.1kW/m3/min, the efficiency is higher than that of the 0.12kW/m3/min model.

4. parameter units and measurement tools

Parameters	unit	measuring tools
power	kW	power meter
pressure	MPa	pressure gauge
temperature	K	thermometer
exhaust volume	m³/min	flowmeter

through the above formulas and examples, you can choose to calculate in detail or simplify the estimation of air compressor efficiency according to actual needs.