How to Calculate Polytropic Efficiency

Equation for polytropic efficiency
••• Public Domain; created by author

Polytropic efficiency is a value used to describe the efficiency of a compressor. A polytropic process is more difficult to analyze than a system under the isentropic or adiabatic assumptions. The difficulty arises from the fact that heat flows in and out of the system, and this added energy changes some of the basic gas properties, specifically the ratio of specific heats. For air, this value is a constant equal to 1.4. For a polytropic process, each new calculation requires a new value for this ratio.

    Obtain the pressure ratio and density ration across the compressor stage you are measuring. These can come from measurements taken at inlet and outlet positions, or you can calculate them based on your compressor's design characteristics. These values are from compressibility tables, just to illustrate the process: p2/p1 = 4.5 rho2/rho1 = 2.667

    Calculate the value for the polytropic ration of specific heats by dividing the natural logarithm of the pressure ratio by the natural logarithm of the density ratio. In this example, "n" represent this ratio. n = 1.504077/0.980954 n = 1.533927

    Determine the value for the ratio of specific heats for the gas you are using in your compressor. For air, the value is gamma = 1.4.

    Use "n" and gamma to calculate the polytropic efficiency, or eta. eta = (n(gamma - 1))/(gamma(n - 1)) eta = (1.533927_0.4)/(1.4_0.533927) eta = 0.821

    Convert the polytropic efficiency value to a percentage for reporting purposes, or leave it as is if you intend to use it in further calculations. eta = 0.821*100 eta = 82.1 percent

    Tips

    • Keep as many decimal places as practical throughout all of the calculations in order to maintain a high degree of accuracy.

Related Articles

How to Solve for Volume
How to Calculate Wobbe Index
How to Convert SCFM to CFM
How to Calculate Condensate Flow From AC Units
How to Calculate Heat Loss During Pipeline Depressurization
How to Convert Stokes to Poise
How to Calculate Steam Velocity
What Is a Centrifugal Blower?
How to Convert Vapor Pressure to Concentration
How to Convert CV to GPM
How to Calculate the Temperature Drop Due to a Pressure...
What Is the Density of CO2?
How to Calculate Boiler Heat Input Rate
How to Calculate Volume at STP
How to Calculate Refrigerant Amounts
How to Calculate Duct Airflow
How to Calculate Tons of Cooling for a Cooling Tower
How to Convert Moles to Pressure
How to Convert BTU to KW

Dont Go!

We Have More Great Sciencing Articles!