Centrifugal Compressor: Absolute Velocity Calculation

How can I calculate the absolute velocity of air at the outlet of a centrifugal compressor if I have:

Diameter of impeller
RPM
Slip factor

I've been reading for weeks and cannot seem to find the answer to this question. For anyone who is familiar with the subject, I'm sure you know about the blade angle, slip factor, radial and tangential components of flow velocity, and absolute flow angle. It's the absolute flow angle that I cannot find any formulas for. Knowing this, I'd be able to calculate the absolute velocity if I know the tangential velocity of the gas, which is a function of the slip factor and tip speed. I can find nothing that relates the radial component of the flow velocity to the RPM or tip speed of the impeller. Any help would be appreciated.

Assuming that your term "centrifugal compressor" refers to a high speed blower as in the simplified diagram below:

The velocity of the air at the outlet is a function of flow rate and outlet flow area. The flow rate is a function of the back pressure, where the function is shown by the fan curve. Search that term, the Aerovent link is a particularly good introduction: https://www.aerovent.com/wp-content/uploads/2018/12/Understanding-Fan-Curves-FE-2000.pdf.

What is the "slip factor"? Air flow around impeller vanes is analyzed using velocity triangles, such as are found using search terms blower velocity triangle. The book Centrifugal and Axial Flow Pumps, 2nd Edition, by A. J. Stepanoff has an entire chapter on the subject. It is a good resource if you want to get deeper into the subject than a simple internet search. The analysis of a blower is identical to the analysis of a pump until you get into compressible flow. Air, or any gas, is merely a low density fluid.

jrmichler said:

Assuming that your term "centrifugal compressor" refers to a high speed blower as in the simplified diagram below:
View attachment 339348
The velocity of the air at the outlet is a function of flow rate and outlet flow area. The flow rate is a function of the back pressure, where the function is shown by the fan curve. Search that term, the Aerovent link is a particularly good introduction: https://www.aerovent.com/wp-content/uploads/2018/12/Understanding-Fan-Curves-FE-2000.pdf.

What is the "slip factor"? Air flow around impeller vanes is analyzed using velocity triangles, such as are found using search terms blower velocity triangle. The book Centrifugal and Axial Flow Pumps, 2nd Edition, by A. J. Stepanoff has an entire chapter on the subject. It is a good resource if you want to get deeper into the subject than a simple internet search. The analysis of a blower is identical to the analysis of a pump until you get into compressible flow. Air, or any gas, is merely a low density fluid.

Thanks for the book suggestion. Yeah, I'm interested in a compressor specifically. The slip factor is the ratio between the tip speed (tangential) of the impeller and the actual tangential component of the absolute velocity of the gas. Again, I don't have a mass or volumetric flow rate. I want to be able to determine that from the impeller geometry and angular velocity (RPM). I'm familiar with the velocity triangles, but just like with any right triangle, you need at least two sides or an angle and a side to determine the other sides. The slip factor can give you the tangential component of the absolute velocity based on the RPM and impeller tip velocity, but the angle of the fluid exit and/or the radial component of the velocity is still not known, therefore no absolute velocity can be determined and no flow rate or pressure. The flow rate is based on the radial component of the absolute velocity. The absolute velocity of the gas at the outlet of the impeller has to be known to determine the performance.

I did not do this for a long time and I don't have a lot of time to study this problem at this time, so it would be easier for me - and others I'm sure - if you develop the problem here for us. We may help out better this way.

If I understand what you want to do, You have to go with the velocity triangles as @jrmichler mentioned. This will give you a set of equations and unknowns. You may have other equations that would join in regarding desired pressure, mass air flow, and power. You must have one equation for each unknown. That is the way to start a problem like that.

Do the work - write the equations, identify the unknowns, make the drawings, etc. - and come back to us as you go along if needed.

I must make a correction, the slip factor is the ratio between ideal whirl velocity and the actual whirl velocity, also called tangential component of the absolute velocity. Apparently I can't edit my reply above.

jack action said:

I did not do this for a long time and I don't have a lot of time to study this problem at this time, so it would be easier for me - and others I'm sure - if you develop the problem here for us. We may help out better this way.

If I understand what you want to do, You have to go with the velocity triangles as @jrmichler mentioned. This will give you a set of equations and unknowns. You may have other equations that would join in regarding desired pressure, mass air flow, and power. You must have one equation for each unknown. That is the way to start a problem like that.

Do the work - write the equations, identify the unknowns, make the drawings, etc. - and come back to us as you go along if needed.

Yes, the velocity triangle is the problem. At this point, most of it is unknown so I'll have to do some more reading.