Tuesday, July 04, 2006

Where's a physicist when you need one?

Given that I owe my first class degree in mathematics to a big bet on being able to master "dynamics", I shouldn't admit that I couldn't answer this question immediately. However, I thought I'd throw it open.

I was in a bar on Saturday afternoon watching the England vs Portugal match.

I say "watching". I was, for the most part, bored out of my mind. I find it very, very hard to get excited by football. I watched the penalties; they were fun. I grasped, correctly, that it was not appropriate to demonstrate my enjoyment of the penalties; everybody else there was taking them extraordinarily seriously.

I digress. My point is this: I found myself interested by the fan that was being used to circulate air in the warm bar.

It was one of those fans that moves about a vertical axis, hence blowing air across an arc.

I was sitting about three metres away.

I observed that it took four seconds for me to feel the rush of the cool air from the time the fan was directly pointing at me.

From this, I think it is safe to surmise that the air was being pushed across the room at 0.75 ms-1.

My question is this: do we have enough information to calculate how fast the blades were spinning? And if so, what was that speed?

(Like I say, I was bored...)

4 comments:

Ben said...

How about using conservation of energy and momentum? We could make the very dodgy assumptions that all the momentum from the blades is given to the air, creating a cylinder of air moving uniformly at 3/4 m/s perpendicular to the fan.

I think this leads to an angular velocity of w = 9/16r rad/s, where r is the length of the blades (and the radius of the cylinder). Then if r = 0.25 m, we get w = 2.25 rad/s, i.e. about 2.8 revolutions per second. Presumably losses in practice would mean the fan was actually going a bit faster.

Do you see how fast the fan was actually going?

Richard Brown said...

The fan was going fast enough that the bladed were blurry. 2-3 revolutions per second sounds entirely reasonable.

Could you show your working please? :-p

Ben said...

Grr, I thought you might ask me that. How do you expect me to do maths in a text box that doesn't even let me do superscripts? You'll have to grab it here.

Richard Brown said...

GENIUS!!