## Monday, June 11, 2007

### Pipe Dreams

I'm sure you all remember your physics and math courses, right?

Two identical tanks full of water are being drained at the same time. One of the tanks has one -two centimeter circular drain outlet and the other has two -one centimeter circular drain outlets. Will one of the tanks empty faster than the other?

1. I think the 2cm drain tank will drain faster. It has twice the drain area.

2. The one with the 2cm hole will drain fastest. This is b/c area is a squared funstion. Two squared is 4, whereas 1 sqaured is 1, and two of those will equal 2. So the one with one hole will drain faster.

3. Looks like all that time spent by your teachers didn't go to waste... :-)

4. The ratio would be

Let the 1cm radius = r

(pi)(2r)^2:2[(pi)(r)^2]
(2r)^2:2(r^2)
4(r^2):2(r^2)
4:2
2:1

So, the 2cm hole is twice as big as two 1cm holes.

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