1. The load on a fan is the pneumatic one + the losses.
2. The fan can run in vacuum assuming you mean an electric fan - but
a) No air to displace hence it is not a fan
b) The losses can not be dissipated (no cooling air) hence the fan will quickly fail due to over heat.
3. These are not electrical question and are more of a mechanical (Fluid mechanics) and Heat+thermodynamics
4. Of course it is a bit rude, but the first word could have been rephrased.
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The power needed for any fluid mover is the increase in pressure times the volumetric flowrate, all expressed in compatible units.
A hypothetical fan running in a vacuum, therefore, will have no pressure change and no volumetric flowrate, as there is no fluid to move. So the power needed, apart from that required to overcome seal and bearing resistance, will be zero.
The concept of wanting to run a fan in a vacuum, however, is awe-inspiring....
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