A couple of ball check valves are used for air input and output. The resulting pump isn’t the prettiest of pumps, and it could probably do with a bit of balancing as it rattles somewhat.
HVAC Commissioning Chapter 13 Water Balance Procedures Chapter 14. Centrifugal Pumps and Pipe Systems Chapter 15. Analog and Digital Automatic Controls PART III Chapter 16. Fluid Flow, Psychrometric, ...