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If a bucket has a 4mm hole in the bottom allowing water to leak out at a rate of 1 pint a minute, does that mean that a 8mm hole will allow water to leak out at 2 pints a minute?

My gut feeling is no, it will leak out faster, but I don't really understand why.

If I'm right and it is faster, how would we calculate how big the hole should be for 2 pints per minute?

4mm being what? The radius, diameter, circumference or 4mm² being the area of the hole?

Sorry, obv missing relevant info.

Diameter.

4mm and 8mm being the diameter of the hole?  If that's the case, then the 8mm hole will let more than double the amount of water out per minute as the area of the hole is what's important.

The area is πr².

4mm diameter gives a r=2mm

3.14 x 2² = 12.56mm²

8mm diameter gives a r=4mm

3.14 x 4² = 50.24mm²

So the water will come out at 4 times the rate.

think this is maybe physics rather than maths?

If you removed the entire bottom of the bucket, the water would fall as fast as possible (can't remember what speed that is).  

Aren't there other forces at play?

OK. I believe you, but I want to understand your answer, so first of all, what does "The area is πr2" mean and how do you know that it's so?

I think we were assuming everything else was a constant and that if you have a hole that's twice as big (or two holes the same size instead of one), then the water would flow at twice the rate. Having a hole with twice the diameter is the same as having a hole 4 times as big, or four holes of the same size as the original one.  Therefore the flow rate would be 4x the original?

If 4mm is the diameter which seems likely since Tom would have used a 4mm drill then the area of the hole would be 4pi
To double the flow needs an 8pi hole ( pi x 2 ^2) so the diameter needs to be such that the square of half of it is 8
Sq rt of 8 is approx 2.82 so the hole needa to be 5.64mm ish

Surely not if the bucket was bucket shaped. (i.e. conical)

http://www.efunda.com/formulae/fluids/draining_tank.cfm#calc

Cliffs: Boshi is right and the rate for a given hole size depends on how deep the water in the bucket is.

See, that's really surprising. I'm very interested in pi holes.

We're assuming a constant flow rate regardless of depth.

How do we arrive at the fact that a 5.64mm hole is 8pi?

And would it be the same if it was metres or kilometers instead of mm?

It must be a bugger when you're packaging ice cream. Twice as much to fill a slightly bigger tub.

Thats a point - the depth of the water reduces faster with the larger hole.  So I don't think its a linear relationship between hole size and speed of evacuation.

Ah, I'm with you now. So in the real world, with a constant pressure David's 5.64mm hole would need to be slightly larger to allow for a slower flow rate?