In reply to Green Porridge:
> (In reply to Jack B)
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> But the intake must be the same as the exhaust - you have the same mass flow front and back, otherwise you very quickly get a load of backed up air or a vacuum in the fan.
The mass flow is the same, what I meant was the geometry (and thus force imparted) will be different.
> The units here make me slightly nervous (mass x velocity is a momentum, not a force), but even if is the mass flow, rather than just mass, then you've got to be double counting.
mv is also an impulse. I was considering the impulse given by a 'chunk' of air, purely to try and simplify the maths I had to type. Perhaps I should have just tagged 'per second' onto everything and used force instead of impulse.
> You are overcomplicating it. You're right that the sideways momentums "cancel each other out" leaving you with no sideways force on the fan. Talking about force from the inlet and outlet isn't necessary (and doesn't really make much sense). In the end, the rotating blades of the fan impart a force on the air molecules, causing a rate of change of momentum (dp/dt). It's just this rate of change of momentum that's important, as that's our force.
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I'm a physicist, overcomplicating things is what we do. Ultimately talking about force at the inlet and outlet makes sense if you think of the fan as a black box and you just integrate over some surface enclosing it to get the impulse it's imparting to the air, and thus that the air imparts to it.
I chose that approach rather than thinking about what happens at the fan blades because that's actually horribly complicated if you get into it. The (small) pressure difference across the blade becomes important, and the maths becomes horrific. By integrating over a surface 'far enough' from the fan you can have the same air pressure everywhere you are doing the integral.
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> I totally understand that normally the velocity at the inlet to a fan seems much less than the velocity at the outlet, and you're right, this is because the air is sucked in from a hemisphere, but comes out in more of a beam shape. However, the mass flow is the same, and if you stick that fan in a long tunnel, the speed before the fan, and the speed after the fan are the same (assuming no massive pressure differences, or cross sectional area differences). It's how most open circuit wind tunnels work, you use the fan to "suck" rather than "blow" air through the wind tunnel - you achieve the same speed, but with much less turbulence.
This is true, but the hemisphere thing is crucial to making this work. If the fan sucked in air in a 'beam' from behind it, the boat wouldn't move (or would move backwards). The boat only moves forwards if the air reflected off the sail has more backwards momentum than the air sucked into the fan has forwards momentum.
It is important that while the mass flow is the same both sides, and the speed (averaged over all the air) is the same both sides, the velocity (averaged over all the air) is less on the intake side.
Either way, I think Mr Blackett has got his head around it now...