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...)


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...