Submerged Weir Discharge Computation

[sswan60]

What is the best method to compute Q over a submerged weir?

My discharge is 344 cfs, weir length = 40'. Tailwater is 1.4' above the weir (H2). Assume a sharp crested weir.

The procedure in HEC-RAS results in no reduction, so H1 = 2.0'

The equation developed by Brater & King, '76 results in H1 = 2.3'

Which is the better answer?

 

[psmart]

Obviously, there should be some reduction in flow (or increase in head) due to the tailwater. The submerged weir equation by Brater & King is reasonable. Another approach is to calculate weir flow for the flow area above the tailwater, and add constant-head orifice flow for the submerged area. Doing this with HydroCAD I get a head of 2.22' vs 2.26' for the submergence equation, which is pretty good agreement.

Peter Smart
HydroCAD Software

http://www.hydrocad.net

 

[LincolnPE]

Just FYI > Attached is some relatively new (HEC 2010) research.

 

[sswan60]

I said "developed by Brater & King," but that's not really the case. Brater and King published work done in '47 by Villemonte. Possibly the method used in HEC-RAS is based on something more recent?

 

[sswan60]

>Possibly the method used in HEC-RAS is based on something more recent?
As suggested by Lincoln. Just noticed your post, thanks.

 

[GrahamC001]

Don't know if you are still interested, but I did some investigation of this a couple of years back. We were dealing with a weir operating v close to modular limit, so the position of this and further drowning effects was important.

I compared formulae/charts provided by Ackers (1971); King and Brater (Villemonte) (1963); Davis (1952); Bligh (1927) and Bos (1989). The comparison showed that there are significant differences in the results obtained by these different approaches. Withough going into too much detail I found that if you are using the Villemonte equation then you are probably getting results at the conservative end of the scale (ie indicating that drowning has a greater impact on discharge, with a lower modular limit). The more recent Ackers (and Bos), on the other hand, indicates that the modular limit is at around 0.9 and flow rates decrease rapidly above this. It sounds like this is more akin to what HEC-RAS is telling you.

So, it comes down to whether you need to be conservative or are struggling to get something to work. Personally I put a lot of faith in Bos in these things, but it is aimed at flow measurement structures and so may give an optimistic view of things on other less "refined" weirs. Hope this provides some useful context.

 

[sswan60]

One thing I learned is that the HEC-RAS procedure used is based on a broad crested weir which is not affected as much by submergence as a sharp crested weir.