Title: More mafs. Post by: RED-DOG on April 02, 2015, 05:23:58 PM 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? Title: Re: More mafs. Post by: Tal on April 02, 2015, 05:26:32 PM 4mm being what? The radius, diameter, circumference or 4mm2 being the area of the hole?
Title: Re: More mafs. Post by: RED-DOG on April 02, 2015, 05:30:19 PM 4mm being what? The radius, diameter, circumference or 4mm2 being the area of the hole? Sorry, obv missing relevant info. Diameter. Title: Re: More mafs. Post by: kinboshi on April 02, 2015, 05:30:23 PM 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. Title: Re: More mafs. Post by: doubleup on April 02, 2015, 05:32:56 PM 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? Title: Re: More mafs. Post by: RED-DOG on April 02, 2015, 05:33:49 PM 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? Title: Re: More mafs. Post by: kinboshi on April 02, 2015, 05:35:23 PM 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? Title: Re: More mafs. Post by: david3103 on April 02, 2015, 05:36:13 PM 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 Title: Re: More mafs. Post by: RED-DOG on April 02, 2015, 05:36:25 PM 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) Title: Re: More mafs. Post by: Longines on April 02, 2015, 05:37:29 PM 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. Title: Re: More mafs. Post by: RED-DOG on April 02, 2015, 05:39:10 PM 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. Title: Re: More mafs. Post by: RED-DOG on April 02, 2015, 05:40:28 PM 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. We're assuming a constant flow rate regardless of depth. Title: Re: More mafs. Post by: RED-DOG on April 02, 2015, 05:41:52 PM 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? Title: Re: More mafs. Post by: RED-DOG on April 02, 2015, 05:43:15 PM And would it be the same if it was metres or kilometers instead of mm?
Title: Re: More mafs. Post by: RED-DOG on April 02, 2015, 05:44:46 PM It must be a bugger when you're packaging ice cream. Twice as much to fill a slightly bigger tub.
Title: Re: More mafs. Post by: doubleup on April 02, 2015, 05:45:48 PM 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. We're assuming a constant flow rate regardless of depth. 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. Title: Re: More mafs. Post by: RED-DOG on April 02, 2015, 05:49:08 PM 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. We're assuming a constant flow rate regardless of depth. 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? |