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RED-DOG
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« on: April 02, 2015, 05:23:58 PM » |
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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?
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Try to be the person your dog thinks you are.
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Tal
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« Reply #1 on: April 02, 2015, 05:26:32 PM » |
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4mm being what? The radius, diameter, circumference or 4mm2 being the area of the hole?
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"You must take your opponent into a deep, dark forest, where 2+2=5, and the path leading out is only wide enough for one"
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RED-DOG
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« Reply #2 on: April 02, 2015, 05:30:19 PM » |
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4mm being what? The radius, diameter, circumference or 4mm2 being the area of the hole?
Sorry, obv missing relevant info. Diameter. |
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Try to be the person your dog thinks you are.
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kinboshi
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« Reply #3 on: April 02, 2015, 05:30:23 PM » |
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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.
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'The meme for blind faith secures its own perpetuation by the simple unconscious expedient of discouraging rational inquiry.'
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doubleup
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« Reply #4 on: April 02, 2015, 05:32:56 PM » |
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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?
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RED-DOG
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« Reply #5 on: April 02, 2015, 05:33:49 PM » |
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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.
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? |
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Try to be the person your dog thinks you are.
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kinboshi
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« Reply #6 on: April 02, 2015, 05:35:23 PM » |
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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?
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? |
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'The meme for blind faith secures its own perpetuation by the simple unconscious expedient of discouraging rational inquiry.'
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david3103
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« Reply #7 on: April 02, 2015, 05:36:13 PM » |
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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
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It's more about the winning than the winnings
5 November 2012 - Kinboshi says "Best post ever on blonde thumbs up"
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RED-DOG
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« Reply #8 on: April 02, 2015, 05:36:25 PM » |
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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?
Surely not if the bucket was bucket shaped. (i.e. conical) |
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Try to be the person your dog thinks you are.
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RED-DOG
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« Reply #10 on: April 02, 2015, 05:39:10 PM » |
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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
See, that's really surprising. I'm very interested in pi holes. |
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Try to be the person your dog thinks you are.
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RED-DOG
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« Reply #11 on: April 02, 2015, 05:40:28 PM » |
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We're assuming a constant flow rate regardless of depth. |
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Try to be the person your dog thinks you are.
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RED-DOG
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« Reply #12 on: April 02, 2015, 05:41:52 PM » |
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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
See, that's really surprising. I'm very interested in pi holes. How do we arrive at the fact that a 5.64mm hole is 8pi? |
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RED-DOG
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« Reply #13 on: April 02, 2015, 05:43:15 PM » |
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And would it be the same if it was metres or kilometers instead of mm?
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RED-DOG
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« Reply #14 on: April 02, 2015, 05:44:46 PM » |
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It must be a bugger when you're packaging ice cream. Twice as much to fill a slightly bigger tub.
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Try to be the person your dog thinks you are.
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