Fluid Dynamics and the Francis Formula

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Hey all...

I'm trying to write a technical report and one part involves calculating the rate of flow of water through a straight horizontal weir. Searching on the web has led me to the Francis formula, which seems to be pretty straightforward. The problem I have is that my specific application has a much lower head (height of water) then used in any of the sample problems and on the net with the Francis formula. In addition, the Francis formula seems to apply to water flowing over a weir, in almost waterfall like fashion. For my purposes, the water will cascade down a surface... I don't know if this will affect the flow rate, or if I can use the formula in my situation.

So basically, I want to know if there is a threshold that is "safe", in which I would be okay using the formula (getting reasonable values). I would really appreciate all the information I could get on the Francis formula (and any other ones that apply).

Thanks,
Preet
 

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  • #2
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I'm sorry for bumping my post up so quickly, but I don't think I really explained what I was looking for properly...

Normal applications of weirs tend to require that the water that escapes from the weir does not cling to the surface (as seen in 1. [attached]):

My application requires they DO cling to the surface (as seen in 2.). Unfortunately I cannot find any information on how to calculate flow rate with a clinging nape since in general that is a situation that would be avoided.

In addition, I see a few different versions of the "Francis formula" which is the most common method I see being used to calculate flow rate from weirs, and I've read specifically that a clinging nape distorts the accuracy of the results heavily.

The formula I'm looking for is a relation between the Width of the weir, Head (height) of water on top of weir plate, and Flow Rate of water.

I'm having a lot of trouble finding good relevant information, so I'd appreciate any advice or links.

Thanks,
Preet
 

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  • #3
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I found a really helpful book, which in one part, covers my situation in detail. I posted to recommend you check the book out (it's free due to copyright expiry).

The book is called "Hydraulics and its Applications" by A.H. Gibson

http://www.archive.org/details/hydraulicsapps00gibsrich
 

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