Applicabilty of orifice flow

[SMIAH]

Hello,

I'm working on a project with an orifice plate placed in front of a culvert to control the released flow rate from a retention pond. The size of the culvert is a 36'' RCP and the orifice plate centered on this pipe is a 27''.
The max WSEL above the center of the orifice plate will be 5'.

Would you calculate the released flow rate roughly/simply by using an orifice flow equation (i.e. Q = CdA(2gh)^0.5)?
Does this equation holds for an orifice diameter over 12'' ?
Does it hold for a WSEL higher than 1.5D?
What else to do?

Thanks,

Regards

 

[pinkpig]

your head water is only 5 ft above center of orifice but your orifice is 27" diameter, in this case, the headwater elevation changes greatly at different vertical heights of orifice. You can integrate to get a total Q,Q=sigma delta Q, delta Q=Cd*delta A sqrt(2gh),delta A = delta h*width, wdith itself is a function of h.

 

[SMIAH]

Not sure to follow you on that one. Can you explain a little more?

 

[cvg]

you could integrate as suggested, however according to Brater and King, the equation you cite is recommended and adjustment to compensate for low heads and large orifices is made by adjusting the C coefficient. Generally, the C coefficient increases with lower heads and eventually when the head is low enough the orifice performs like a weir.

 

[SMIAH]

Worked it that way (weir flow for <0.5D and orifice flow above).

Howewer : (from page 8-22, Hydraulic Engineering Circular No. 22, Second Edition)

Pipes greater than 0.3 m (1 ft) in diameter should be analyzed as a discharge pipe with headwater and tailwater effects taken into account, not just as an orifice.

 

[Drew08]

Certainly, don't over think it, keep it simple. The nuances in adjusting the C value, or applying it to large diameter pipes, or integrating anything, are far outweighed by the uncertainty in the hydrology you used to develop the inflow hydrograph. Odds are you applied ample factor of safety in choosing CN, Tc, rainfall, hyetograph, etc that a few cfs error in the discharge as a result of simplification is small potatoes. Save yourself time and headache and apply the orifice equation as written, linear interpolate between Q = 0 and Q at H = 0.2D.

 

[SMIAH]

I did it. Just used weir equation under 0,5D correcting the length.

I was wondering though if I had to check it with another equation/condition. In my case (isn't always?), it's pretty important to access the real (i.e. more accurate possible) flow rate discharged from the pond.

True about anything from Q = 0 to Q at H = 0.2D though!

 

[beej67]

The 'normal' orifice equation is only valid when the orifice is small in relation to the head on it. When the orifice is large relative to the head, the streamlines of the flow across the orifice area are not perpendicular to the orifice, so the continuity equation ends up a little bit wonky. Attached are some lecture notes from when I cover this issue in my hydrology class. Of particular interest to you is page 2-4. Your orifice is a "large orifice" when submerged and a "sharp crested weir with end contractions" when not submerged. If your orifice is circular on top of that, the derivation gets tougher than what's shown, but it's essentially the same process.

The other way to do this without the calculus, if you still want to build up from base principles, is use DOT culvert design nomagraphs. For your inlet control check, select a pipe equal to your orifice diameter, and for your outlet control check, select a pipe equal to your pipe diameter. That's probably how I'd do it, given your situation. It's easy, clean, and produces a record of your procedure that old farts will understand.



Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East -

http://www.campbellcivil.com

 

[SMIAH]

Thanks beej67.

I'll do that.

Wonder what it will look like vs simple orifice calculation.

 

[SMIAH]

So it really ends up to a weir equation (Q=CLH^1.5).
With 2/3*Cd*(2g)^0.5 = C
I could have a L for each H. Averaging L for each H... And it wouldn't even be right.
Ouf!

Why then do people use large orifice for detention pond outlet structure. They're calculating it as a small orifice without questionning.

 

[beej67]

Why then do people use large orifice for detention pond outlet structure. They're calculating it as a small orifice without questionning

I imagine some of the people who do it know what they're doing and have accounted for it. Others probably don't know the math and are leaning on hydrology software to think for them. I'd hate to pass judgment on any given engineer or his design without reviewing the design, but I will say I've seen a lot of designs that use large orifices on small reservoirs when they should have used weirs.

Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East -

http://www.campbellcivil.com

 

[psmart]

I've seen a lot of designs that use large orifices on small reservoirs when they should have used weirs.

Ideally, your hydrology software will automatically use weir flow under low-head conditions.

Peter Smart
HydroCAD Software

http://www.hydrocad.net

 

[SMIAH]

beej76 : The equation on your pdf looks similar to a gate-flow structure type as seen on a dam.
psmart: HydroCAD won't use a weir flow for a large orifice though (e.g. above a radius of 12''), isn't?

For the design I am refering to, the orifice really looks like an outlet-culvert with a smaller size and a higher inlet elevation than the one entering the basin. I had doubts about the applicability of plain simple orifice flow equation for it and beej76 confirmed what I was thinking.
Now I have to keep Drew08's comment in mind about not over thinking it and keeping it simple

But I wonder what would be the outcome of calculations. The difference in Qout/WSEL for a circular large orifice vs small one...

 

[psmart]

Regardless of the orifice size, HydroCAD will transition or weir flow at low heads. Calculations are documented in the Owner's Manual and help system.


Peter Smart
HydroCAD Software

http://www.hydrocad.net

 

[beej67]

Gate flow is basically a big rectangular orifice.

If you're hung up on this, there's software that can do it for you. HydroCAD can do it, for instance (nod to Peter) as can SWMM. For HydroCAD, you use a "pond node" without any actual storage, and you do a 2 stage structure, with the orifice routed to the culvert.



Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East -

http://www.campbellcivil.com