換水份量 - 鬧市冰室

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換水份量

iczfirz

"challenge"

文章: 14186
來自: 我回來了

1 于 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?

iczfirz 修改于 2002-06-12 19:11

^{問題或承受過不相信拋下過最後決定一雙肩膊別太肩膊
三十一畫：此數大吉，名利雙收，漸進向上，大業成就。（吉）}

林哥仔

景霧處(魚缸交流組)

文章: 1421
來自: 紅磡

2 于 2002-06-12 20:41

咁樣有機會一來即去........我唸最多只有25--50%

人生就如汪洋中的一尾小魚,
只要能樂天知命,
天地自可任縱橫!

iczfirz

"challenge"

文章: 14186
來自: 我回來了

3 于 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?

^{問題或承受過不相信拋下過最後決定一雙肩膊別太肩膊
三十一畫：此數大吉，名利雙收，漸進向上，大業成就。（吉）}

林哥仔

景霧處(魚缸交流組)

文章: 1421
來自: 紅磡

4 于 2002-06-12 22:27

<<<<<係呀>>>>>

人生就如汪洋中的一尾小魚,
只要能樂天知命,
天地自可任縱橫!

mirrorguy

文章: 45

5 于 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) ].

mirrorguy 修改于 2002-06-13 20:52

Gundaman

文章: 750

6 于 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!

The 50/50/90 Rule: Anytime you have a 50/50 chance of getting something right, there's a 90% probability you'll get it wrong!

iczfirz

"challenge"

文章: 14186
來自: 我回來了

7 于 2002-06-13 14:26

厲害

好得人驚

但我想知.. 呢條係中幾既數呀?

^{問題或承受過不相信拋下過最後決定一雙肩膊別太肩膊
三十一畫：此數大吉，名利雙收，漸進向上，大業成就。（吉）}

mirrorguy

文章: 45

8 于 2002-06-13 14:31

應該係大一數學.

Gundaman

文章: 750

9 于 2002-06-13 14:33

Pure maths in matriculation.

The 50/50/90 Rule: Anytime you have a 50/50 chance of getting something right, there's a 90% probability you'll get it wrong!

omicron

行行企企食飯幾味:p

文章: 366
來自: 清水灣火雞大學

10 于 2002-06-13 17:30

wa....鏡叔叔....小兄五體投地.........

omi+omi+omi=omix3
→不求盲目崇拜←

Wilbert

文章: 8

11 于 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.

:-)

iczfirz

"challenge"

文章: 14186
來自: 我回來了

12 于 2002-07-15 15:34

Wilbert: 你諗得太多喇..

我係開住個沙缸上水泵黎換架

^{問題或承受過不相信拋下過最後決定一雙肩膊別太肩膊
三十一畫：此數大吉，名利雙收，漸進向上，大業成就。（吉）}

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