How does the fan in a vacuum cleaner boost the pressure back up so that the air flowing through the vacuum cleaner the air will go back into the room?
The fan is a rotating assembly of ramps. As the ramps move, they sweep the air from one side of the fan to the other and do work on that air. The air either accelerates as the fan blades spin past, or its pressure builds up. Either way, its total energy increases. The fan can take low-pressure air from one side and whisk it over to the other side where the pressure is higher. It can push air against the natural direction of flow (from high pressure to low pressure). It’s essentially a pump for air.