# How to convert absolute discharge pressure to polytropic head?

By | August 16, 2013

Many of the compressor vendors provide performance curves in terms of absolute discharge pressure vs actual suction flow however, most of the process simulation software require compressor head data not discharge pressure (absolute).

Following are the steps to convert the discharge pressure to polytropic head:

Step1: Get the absolute discharge pressure (Pd) and efficiency (ε) vs. actual volumetric flowrate (v) data.

You may have to digitize the performance curve using Graph Digitizer programs. There are many available online such as GetData.

Step2: Find out the inlet conditions at each stage:

• Suction Temperature: T1
• Suction Pressure: Ps
• Discharge Pressure: Pd
• Average Isentropic Exponent, Cp/Cv: k
• Molecular Weight: MW
• Polytropic Efficiency: ηp

Step 3 : Calculate the polytropic exponent (n) using equation below:

$\frac {n}{n-1} = \frac {k}{k-1} \; \eta_p$

Step 4 : Conversion of Absolute discharge pressure to Polytropic Head:

$H_p = \frac {Z_{avg} \; R \; T_1}{MW \; m} \; (r^m - 1)$

where:

$m = \frac {n-1}{n}$

$r = \frac {P_d}{P_s}$

$Z_{avg} = \frac {Z_d + Z_s}{2}$

Zs = Suction Compressibility Factor.

Zd = Discharge Compressibility Factor.

R = Universal gas Constant.

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