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Topic: 換水份量

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Posted by: iczfirz Posted on: 2002-06-12 14:07 缸係150L.. 換水的水箱50L. 換水水箱用氣喉虹吸管引水入沙缸.. 沙缸的水位就會升高. 同一時間沙缸用自制overflow管放走升高左的水.. 咁... 我咁做.. 實際換左幾多水?

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Posted by: 林哥仔 Posted on: 2002-06-12 20:41 咁樣有機會一來即去........我唸最多只有25--50%

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Posted by: iczfirz Posted on: 2002-06-12 21:04 點會有50%呢??? 你係指換入果50L水有25L會係番個缸度?

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Posted by: 林哥仔 Posted on: 2002-06-12 22:27 <<<<<係呀>>>>>

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Posted by: mirrorguy
Posted on: 2002-06-13 13:01

Assuming the incoming and outgoing water rates are the same.

Denote the size of the main tank to be M, the size of plastic box to be S. Assume the percentage of new water in the main tank is f(t), a function of time t.

Then during a certain time period from t to t+t1, the balance of new water is given by

S t1 - S t1 f(t) = M f(t+t1) - M f(t)

Let t1 --> 0, we obtain

S (1- f(t)) = M f'(t).

The initial condition is f(0) = 0. Solve the equation we have

f(t) = 1 - e^(-S t/M)

Finally, new water in the main tank is

M [ 1 - e^(-S/M) ].

For the problem proposed by iczfirz, M = 150L, S = 50L. Substitute them into the formula, we have

150 [1 - e^(-1/3) ] = 42.5 L

This means iczfirz had 42.5L new water remaining in the main tank. Waaa...., that's more than everybody's expectation!!!

So, next time if you want to change water by using iczfirz's approach, then just use the formula:

M [ 1 - e^(-S/M) ].

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Posted by: Gundaman Posted on: 2002-06-13 14:00 嘩!!! mirrorguy果然是數學高手, 你個仔會考maths冇A1都有A2呀! 勁呀! :O):O)

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Posted by: iczfirz Posted on: 2002-06-13 14:26 厲害:O) 好得人驚:}) 但我想知.. 呢條係中幾既數呀?

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Posted by: mirrorguy Posted on: 2002-06-13 14:31 應該係大一數學.

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Posted by: Gundaman Posted on: 2002-06-13 14:33 Pure maths in matriculation.:)

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Posted by: omicron Posted on: 2002-06-13 17:30 wa....鏡叔叔....小兄五體投地.........:O):O):O):O)

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Posted by: Wilbert Posted on: 2002-07-15 14:20 replacement tank water -> sand sump -> overflow in sand sump -> exit ie. no replacement at all (or just very little). All new clean water will just gone and just very little flow back to main tank. This is an IQ question. Read the initial post very carefully again. :-)

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Posted by: iczfirz Posted on: 2002-07-15 15:34 Wilbert: 你諗得太多喇..:D 我係開住個沙缸上水泵黎換架:D:D

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