Originally Posted by PeterVRC
It wasn't in your first listed equations.....
You said thrust is a result of velocity times volume...... no mention of density.
And I am sure that it is this density is what makes a CS10 different than a lower blade count fan. Not because they could not do the same, but because they don't - due to blade/area design.
And the proof is in that they are quite different results to each other. Irrespective of maths etc.
(same as equal pitched 5 blade props are different results to 2 blade props of that same pitch, running at the same RPM)
You don't need to know the specific maths to know there is a difference.
Whalleyboy asked about efflux velocity and thrust, I answered with the truth that the velocity and thrust are tied together.
Air density should be the same at anytime you test two different fans at the same time so calculation of both fans can be taken at the same density. The rotor moves air by virtue of blade angle of attack displacing air from the inlet side to the exit side of the fan. Number of blades has no effect other than a little friction on the blades surface area. Once air is moving the number of blades do not do anything different than a 3 blade rotor if the rotors have the same blade shape ie angle of attack and geometric twist.
My friend your an engineer who says math and physics do not define the abilities of a fan, does it also not define tires and road interaction? There are friction coefficients that give indication of how much taction the tires have both in dry conditions and wet conditions, these can be mathematically worked to give a good indication of how far it will take to stop a car moving at defined velocity rather well. Physics and math are in every part of engineering that I have been a part of and a part of everyday life.