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Problem: gravity draining tank through sloped pipe, falling head

Problem: gravity draining tank through sloped pipe, falling head

Problem: gravity draining tank through sloped pipe, falling head

(OP)
Hi,

I am trying to model a detention basin as a rectangular tank with a sloped discharge pipe on the bottom. I would like to know the required time for the tank to empty when drained from full. I understand that I need to set up the Bernoulli equation with the Darcy-Weisbach equation and integrate it over the boundary conditions and solve for t, but I am strugling with it. Given are the tank dimensions, pipe material, length, diameter, and fall. Any help would be appreciated. Thanks.  

RE: Problem: gravity draining tank through sloped pipe, falling head

With a lot of perseverance you could probably do it the way you have proposed.  An easier way would be to write a spreadsheet where the flow rate is calculated as a function of height.  Then copy the formulas into 100 (or 1000) rows - one row for each horizontal slice from the top of the tank to the base.  With the calculated flow rate for each slice calculate the time required to drain that slice. The flow rate for each slice would be based on the height to the mid-point of the slice and the flow rate is taken as a constant for that slice.  Add up the times for the 100 slices and you have your answer.

Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com

RE: Problem: gravity draining tank through sloped pipe, falling head

this is a common problem for stormwater engineers, there is free public domain software out there that can do this. (however, you can integrate it also if you would rather do it that way) HEC-1 is one example. SWMMM is another. In addition to the givens you have listed, downstream channel and tailwater conditions will affect the discharge rating curve. Also, your discharge rating curve may vary from orifice to weir flow depending on the depth in the detention basin.

you will need the
discharge rating curve
storage rating curve and
inflow hydrograph (if any)

RE: Problem: gravity draining tank through sloped pipe, falling head

thateb

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RE: Problem: gravity draining tank through sloped pipe, falling head

Made me go through my fluid dynamic books, here's your answer (from "2500 solved problems in fluid mechanics and hydraulics"
 By Jack B. Evett, Cheng Liu):



Hope this would help.  

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