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• # Tank drainage time [bernoulli]

Discussion in 'Calculations' started by Virgule, Feb 24, 2014.

1. ### VirguleActive Member

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Nov 2011
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Hi all,

It's been a while since I've posted.

I have a problem I'm stuck on. I'm trying to calculate how much time it will take for a tank to drain itself into another lower tank. I know the flow will be faster at start and slow down with the lowering liquid column. I'm trying to develop an equation for the height of liquid in terms of time so I can obtain the drainage time, the mean flow as well as the maximal flow in the pipe.

Using the Bernoulli equation between point 2 (first tank's liquid level) and point 1 (just as the liquid exits the pipe - enters the second tank), I developed an equation relating the height of liquid in the first tank to the velocity in the pipe. My problem is both are functions of time. Here's my route so far :

(direct : http://i1189.photobucket.com/albums/z434/Virgule99/Tankdrainage.jpg)

So as you see, I have 2 terms that are functions of t : z(t) and V1(t).

What now ?

2.
3. ### LochnagarWell-Known Member

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Feb 2011
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Hi Virgule,

If you have Fluid Mechanics by Douglas/Gasiorek/Swaffield page 485 / 486 does a worked example of this type of problem. I can email the couple of pages from this book if you want - since posting pictures appears to be difficult on this web site.
Hope this helps.

Gordon.

4. ### VirguleActive Member

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Nov 2011
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Please send me the reference, sent you a private message.

Joined:
Feb 2013
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Hi Gordon
Please do me a favor, Can I have that pages?
Thanks.

6. ### TunaloverMember

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May 2014
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Hey guys this is a public forum so why can't you make the solution PUBLIC? I'd like to see it. I'm sure others would too!
Bruce

7. ### DouglasNew Member

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Oct 2014
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Hi Gordon,

Please could you email me the the pages from the mentioned book?

Many Thanks,

Douglas

8. ### S.K.RoyNew Member

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Nov 2014
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why do you assume that the flow is stream line and not turbulent?

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