How do I calculate the force coming from the centrifugal compressor exhaust?

measure the pressure inside the discharge diffuser with a miniature pitot tube, and the ambient air pressure. the difference will be (delta p). Now measure the area of the discharge diffuser outlet.

the reaction force generated when the blower is running will be approximately

(delta p) x (outlet area).

You could also simply instrument the blower with a force gauge that measures the reaction from the exhaust flow. This has several advantages, as follows:

First, it gives you the actual answer you seek. Second, if you modeled the thrust-generation process mathematically and used that model to predict the behavior of the system, due diligence would require you to verify the correctness of that model by measuring the thrust reaction force in real life. This means you'll be doing this experiment in the future, regardless of the form your model takes.