# Partial vacuum due to a fan

## Main Question or Discussion Point

My understanding is that when a fan begins spinning, a partial vacuum is created. Physically, what creates this partial vacuum? Does the motion of the blades create a void in which there are fewer air molecules than in the ambient air and thus the pressure is lower than the ambient pressure?

## Answers and Replies

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HallsofIvy
Homework Helper
Essentially, yes. The blades of the fan physically push molecules of air out of the way, leaving a partial vacuum behind until more air can move in to replace them.

Thank you. So a spinning fan creates regions where there are less air molecules than ambient air as well as regions where there are more air molecules than ambient air; I guess this will change the density of the macroscopic air particles near the fan? Does this mean that to determine the velocity field for the macroscopic air particles near a spinning fan, you would need to solve the momentum equation for air particles with a variable density field?

rcgldr
Homework Helper
The reduced pressure on the intake side of a fan is due to the intake side surfaces of the fan blade receding away from the air. What would be a void left behind by the fan blade is filled in by air accelerating towards the fan blade, but since the air has momentum, it takes a force to produce the acceleration, and the force is due to a pressure gradient where pressure decreases as the air approaches the intake side of a fan. Once the air crosses the fan. there's a jump in pressure, but not much change in speed. The increased pressure causes the air to continue to accelerate, and after the jump in pressure, the pressure decreases with distance from the output side of the fan. An approximation for the speed of the air as it crosses the fan blades is about 1/2 of the air's "exit" speed, which is the speed of the air as it's pressure returns to ambient.

Here is a link to a Nasa article about propeller's showing a similar effect. Note that the decreasing cross section of the affected air in that article is simplified, ignoring the effects of vicosity at the outer edges of the idealized air flow.

http://www.grc.nasa.gov/WWW/K-12/airplane/propanl.html

Thank you very much.