In this post I want to share you how to calculate ** centrifugal compressor power** since there are so many process engineers are looking for it (and I also don’t know how).

To calculate centrifugal compressor power, we need these gas properties: compressibility factor (Z), molecular weight (MW), inlet gas temperature, inlet gas pressure, outlet gas pressure, adiabatic component (Cp/Cv), and mass flow rate.

Let’s start with an example while I show you step-by-step of the calculation method. In this example, we have these gas properties (I use US units).

*Compressibility factor (Z) = 0.9972*

*Molecular weight (MW) = 18.15*

*Gas constant (R) = 1544/molecular weight*

*Inlet temperature (T1) = 546 deg R*

*Inlet pressure (P1) = 15 psia (don’t forget to use absolute pressure)*

*Outlet pressure (P2) = 60 psia*

**K** (Cp/Cv) = 1,274

*Flow (W) = 0,184 lb/min*

The required data to calculate centrifugal compressor power is **head**. We can use either adiabatic head or polytropic head as long as we use adiabatic efficiency and polytropic efficiency in companion.

In this example, we will calculate power requirement by using adiabatic head, polytropic head, and by process simulator. We want to know if those methods give the same results or not.

**Centrifugal Compressor Power Calculation using Adiabatic Head**

To calculate adiabatic head and power we use equation below.

From the data above, adiabatic head (**Had**) is **74,808.54 ft.lbf/lbm**.

To calculate power, we need **adiabatic efficiency (Ea)**. Adiabatic efficiency is function of type of compressor, rpm, volumetric flow, and adiabatic head. We can determine adiabatic efficiency by using figure below.

Figure above shows that for centrifugal compressor, adiabatic efficiency is ranging from 60% to 80%. For preliminary calculation we choose **70%** adiabatic efficiency.

By using the second equation, we get power requirement is **0.594 hp**.

**Centrifugal Compressor Power Calculation using Polytropic Head**

To calculate power by using polytropic head, we need **polytropic efficiency**. Polytropic efficiency is a function of adiabatic efficiency. Relationship between those efficiency is expressed in equation below.

From equation above, we get polytropic efficiency is **73.99%**. Please note you can change (N-1)/N with (K-1)/KEp.

To calculate polytropic head and power using polytropic data, use equation below.

By using the equation, we get polytropic head is **79,075.11 ft lbf/lbm**. And power requirement is **0.594 hp**, which is exactly the same as previous method.

**Centrifugal Compressor Power Calculation using Process Simulator**

By using process simulator, we get power requirement **0.589 hp**, which is slightly below calculation. But overall, the method is correct.

I think I spend too much time calculating power requirement using both adiabatic approach and polytropic approach. So, it is better to use adiabatic approach only if you are sure enough with the calculation.

One thing that you might need to correct is adiabatic efficiency. In this example, I guessed adiabatic efficiency. It will be more accurate if you calculate specific speed to get exact value of adiabatic efficiency based on graph.

**Bonus Spreadsheet**

You can learn how to calculate centrifugal compressor power calculation by using spreadsheet as attached below. I use example above in this spreadsheet.

Centrifugal compressor power calculation

References:

- Rules of thumb of Chemical Engineers – Carl Brannan
- Perry’s Chemical Engineers’ Handbook

Please also include equations in SI system. Many users dont wnat to start with fps system or less familiar.

Hi, thanks for your feedback. I will do that for the next post! 🙂

Have you uploaded the sheet for the same.

add terminology

We are going to buy Atlas COPC compress three stage but confused over motor requirement.450-8.

We need your help to determine motor required.

Mbak Rifka, Salam….. dimana kira2 saya bisa mendapatkan formula compressibility factor, Z

selama ini hanya mengacu kepada grafik Nelson Obert… atau apakah punya referensi kalkulasi compressor centrifugal, reciprocating compressor dan Turbine khususnya untuk mendapatkan performance

Saya belum cek, Pak Budi. Apakah sudah coba cek di Perry atau Coulson?

Assalamualaikum. I am a graduate student and dealing with the compressor for a purpose of extraction of air mass from a place. I would like to know the flow rate of the air mass through the compressor to the conduit.I am confused about the mathematical formulation for this. Can I have a discussion with you this regard?

Yes sure.. Please send email to me rifka.aisyah@gmail.com

Rifka,

I own a Centrifugal Compressor for which the manufacturarer has provided performance curves which show Politropic Head and POlitropic efficiency vs actual volume flowrate in the suction. At the top of the curves there’s a label which states the suction conditions. Now, my actual conditions do not excatly match those stated, can I still consider that the politropic head and efficiency remain the same and can still use the curves ? Moreover, suppose I decide to change the compresssed gas, are the politropic head and efficiency vs actual volume flow curves still valid?

Thanks!

Take grate care

gracias!

How to calculate Head and Volumetric Flow Rate for Specific Speed calculation and W for Hp?

It is good, could you please provide the calculation of K and z using equations of state

how do i find the same thing but for an expander? I have a turboexpander-compressor system and i m trying to find the horsepower for the expander part.

For a turboexpander you can determine horsepower from total head multiplied by mass flow. Total head is just the difference in enthalpy from inlet to outlet. You can use REFPROP to estimate enthalpies of gas mixtures, single and two phase.

Hello Rifka,

What is the source of the figure which compares the efficiency in function of specific speed for different compressor types?

Regards

Hi Karel,

The source of figure is Perry’s Chemical Engineers’ Handbook 8th Edition Section 10 (Transport and Storage of Fluids).

Good Morning, When can I use Polytrophic efficiency or Adiabatic efficiency?. It is true that for centrifugal air compressors, and single stage centrifugal compressors I should use adiabatic efficiency