1. Formula - isentropic compression. For 1 compressor stage Note : in case of multi … Contact online >>
1. Formula - isentropic compression. For 1 compressor stage Note : in case of multi
Home page COMPRESSORS Reciprocating compressor capacity
The goal of compressor sizing calculations is often to find out the efficiency of the compressor and power required to drive that compressor, given the gas composition, flow rate, temperature & pressure conditions at inlet and outlet pressure requirement.
Let's look at equations frequently used in compressor calculations to determine power and efficiency of the compressor along with their description and significance.
Gas compression can be expressed in terms of pressure and temperature variation as,PVn = constant
A compression process typically following this pressure volume relation is known as polytropic process. If n=1, the process is isothermal (constant temperature). If n=γ=CP/CV, the compression is adiabatic compression (no heat exchange with the surrounding). Most gas compressions generally follow the adiabatic curve. Hence compressor equations are also based on adiabatic curve with n=γ,PVγ = constant
Let subscripts 1 and 2 stand for inlet and outlet process conditions of the compressor. Then the pressure ratio of the compressor is P2/P1.P2/P1 = (V1/V2)n Polytropic compressionP2/P1 = (V1/V2)γ Adiabatic compression
The head developed by the compressor is expressed in following compressor equations.
This head when multiplied by the volumetric flow of gas (Q) gives the compressor power equations.
Adiabatic efficiency of the compressor is calculated as,
Adiabatic efficiency, η = (Actual Polytropic work / Adiabatic work)
Polytropic efficiency or hydraulic efficiency for a compressor is represented by,
These equations will provide us with theoretical values of the power requirement and the thermodynamic efficiencies of the compression process. But then we also need to account for the mechanical efficiencies and loss of power in driving the compressor equipment as well as the electrical motor.
Putting together all these factors, we can finally arrive at practically how much power is going to be needed to drive a compressor with given process parameters.
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Similarly, the actual discharge temperature based on a polytropic path can be estimated by
Solving the above equation for the polytropic path coefficient (n):
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View all posts by: Dr. Mahmood Moshfeghian
thanks for the article,I would also mention that rigorous methods (based on interpolated values such as ASME PTC-10 or numerical integration pin->pout such as Huntington etc.) consider non-contant values for properties from pin->pout,these variations may originate large errors (see the example provided in Huntington’s paper),finally, a procedure can also consider phase equilibria, I know Prode Properties (see ) which includes both Huntington and a proprietary method for solving a polytropic stage with phase equilibria,when there is a change of phase it is difficult to evaluate and adopt a value for efficiency in different conditions…
Please may I know the equation seven. I cannot find the formula for calculating the polytropic path exponent(n). Please can u write the formula for calculating polytropic path exponent
Laurent:You are correct, both temperature and pressure ratios should have been ln(T2/T1) and ln(P2/P1).Thanks.
Hello, used these equations with preos… did not work, gave me an efficiency of 4000…
CAE350 compressor analyzing system is a low cost portable system to test the capacity,power efficiency and unit air consumption of the compressor
Here is the link of a new article, which describes the rigorous calculation of the polytropic efficiency based on thermodynamics of real gases. A comparison with data shown on this website (!) can also be found, under:
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