mo0
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Post by mo0 on Nov 28, 2003 4:03:39 GMT -5
this is a question from my calculus exam for universtiy entrance in New Zealand. "water leaks out of a cylinderical tank through a small hole in the base at a rate proportional to the square root of the depth. Initally the tank is full. After one hour it is half empty. How much time will it take for the tank to empty completly?" and no it didnt get it    |
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Post by nita on Nov 28, 2003 10:37:09 GMT -5
15 mins?
edit = I was going to say 30 mins...but that makes sense to much, so it can't be the answer.. lol
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Pepper
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Post by Pepper on Nov 28, 2003 16:03:53 GMT -5
well if its full it should be 2 hours from start because after 1 hour its half full then after 2 it must be empty? |
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Post by Tulip on Nov 28, 2003 16:17:47 GMT -5
2 more hours
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mo0
New Member
thx to pashy for my siggy :P
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Post by mo0 on Nov 28, 2003 16:42:28 GMT -5
so as the water leaks out of the tank, the depth decreases, but the rate which the water leaks out is proportional to the square root of the depth. In english, the water doesnt leak at a constant rate so it cant be two hours |
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Post by Ohio on Nov 28, 2003 16:48:34 GMT -5
The rate of flow will slow as the depth of the tank decreases. So it will take longer to deplete the last half than the first half. Unfortunately, it is 15 mins till quiting time so I am not going to figure it out right now. If I get bored this weekend I will think about it.
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Post by Dangermouse on Nov 28, 2003 16:55:58 GMT -5
Dont we need to know the depth of the tank  |
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Post by Tulip on Nov 28, 2003 16:58:55 GMT -5
i dunno if i was right but i suspect an additional 2 hours. the depth is not needed if you already know it reduced by 50% in one hour
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Post by lightone on Nov 29, 2003 3:55:18 GMT -5
A little hint, LOL, each half is one hour and there is more than 2 |
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Post by ozzywizard on Nov 29, 2003 6:11:01 GMT -5
I dont think it would ever empty, if it is a small hole in the base then wouldnt you always have little dregws left at the bottom. Thsi is my cheap attempt to get out of working it out.
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Post by Tulip on Nov 29, 2003 9:57:31 GMT -5
ya lightone it is square root, 4 hours total  |
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Fisher
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Post by Fisher on Nov 29, 2003 15:01:28 GMT -5
not exactly sure, couldnt be arsed to work it out, but its either 1 and a half hours or 2 and a half hours:P im suppecting 2 and a half:P lol
cause if you empty a bottle, it starts fast, but the last half takes 1 and a half times the 1st, so 2 and a half hours:P
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Fisher
xTeam
If a Stamped Ever Happens to Run at You, Never Stop and Shout Jumangi, it Doesn't Work!!!!
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Post by Fisher on Jan 20, 2004 14:40:04 GMT -5
answer is.......
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Post by Alexander on Jan 20, 2004 20:36:49 GMT -5
2 and a half hours mins cause it would take longer for the second half to drain cause there aint as much pressure so half the pressure = half on top |
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Post by Dave2002002 on Jan 20, 2004 20:55:09 GMT -5
its nothing related 2 pressure, as the difference between water pressure and air pressure in a closed system is negligible at the depths they would be talking about
say the depth is 10m, then the rate is 3.16m/s. 5m, 2.2m/s and so on.
cant be bothered 2 work it out, but im pretty sure with the rate effected by the depth in this way its gonna take longer than 2 and a half hours...
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