Lets talk orifice coefficients

[beej67]

I'm trying to do some honest research and determine the best orifice coefficient to use in a manufactured grate application.

As I understand it, the orifice coefficient is intended to represent a loss in effective flow area of the orifice due to flow contraction as water moves past the sharp edges of the orifice. This effective flow area reduction drops (therefore the orifice coefficient increases) with two things - how rounded the orifice edges are, and with increasing head on the orifice.

That would tend to make me think that the orifice coefficient for flow through grates, which have multiple parallel sharp edges at fairly low heads, should be reasonably low. Certainly lower than the 0.6 everybody pulls out of their hat as a standard.

I've attached a PDF, that has two pages. One from Sturm's Open Channel Flow, my favorite hydraulics textbook, which shows Table 6-2 taken from FHWA studies on orifice coefficients for inlet headwalls. The table references "Bodhaine 1976," which I have not read. Note that the left hand column of the table is for sharp edged orifices, and the Y axis shows HW/d, which is the ratio of headwater to orifice (in this case culvert) diameter. The highest coefficient it shows is 0.59 - for a head to diameter ratio of 5:1.

The other page is from HEC-22, where they're discussing sag inlets with grates operating in orifice flow. They routinely use an orifice coefficient of 0.67 for the flow through their grates throughout the whole document, even though the relative head on a road inlet is fairly small.

Mixed messages?

Is there a better document to go to, when trying to identify the appropriate orifice coefficient for a grate, or for small diameter orifices? My application is an array of small squares cut into the side of a metal plate, with no edge rounding.



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

http://www.campbellcivil.com

 

[QCANADA]

You may want to check the attached document.

 

[SMIAH]

That 0.67 is... inexplicable to me... it's rather 2/3

The C for weir flow too anyways (3.0).

Well if it's from tests.

 

[SMIAH]

C = 0.66 for a head of 0.2 m over a square orifice of 0.5 cm...

Ah well...

 

[cvg]

among other things, coefficient of discharge will be different depending on:

length of the orifice (thin plate or longer tube)
upstream conditions (is flow converging, diverging upstream)
edge conditions (is there rounding, knife edge etc on the entrance)
exit conditions (how does the flow expand after leaving the orifice)

so, comparing orifice flow testing related to culverts (long tube, no flow expansion, various types of inlet conditions, head/diameter ratio low) with grates (more like a plate, but flow does not expand well) is comparing apples to oranges. Use the FHWA values which were based on actual tests on grates.

 

[beej67]

0.67 is used throughout the HEC-22 document in all of their example problems for pavement drainage as the orifice coefficient. They even drop the "Co" nomenclature for some of their derivations and just build the 0.67 straight into the equation. (like eq 4-35, page 4-67)

Once they start to talk about storage routing in chapter 8, they go back to "(0.40 - 0.60)" for the orifice coefficient. That's also how it's shown in their "list of symbols" in the beginning of the document.

They don't explain (at least as far as I can tell) why they use a different one for pavement drainage through grates. Maybe they were doing all their testing on welded grates with rounded bars?


Thanks Canada, that's helpful, and reaffirmed my thinking to just go with 0.60. I'd love to get to the bottom of this HEC-22 mystery though.

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

http://www.campbellcivil.com

 

[cvg]

I have always used .6 for plate orifices. 0.4 is only recommended for roughly cut (with a torch) through cmp and not for a grate. However, it is apparent there have been tests done with grates giving rates as high as 0.67. Typically though I make a gross assumption that the grate is half clogged so really the difference in capacity between 0.60 and 0.67 then becomes very little.

 

[SMIAH]

True that the difference in capacity may becomes very little for some problems.

But using a C = 0.67 instead of C = 0.60 is increasing the capacity by 12% and this should be explained more extensively in a document as such as the Urban Drainage Design Manual.

 

[beej67]

Maybe it is explained in there somewhere, but I couldn't find it.

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

http://www.campbellcivil.com

 

[cvg]

i would not get too hung up on the values shown in section 8. it is clear they are not for typical grates, but for orifices typically used in basin outlets such as slotted cmp riser pipes and flat plate orifices installed on pipe headwalls.

 

[Ryb01]

speaking of coefficients.....

I can't seem to remember and or recall the conversion factors from imperial to metric for weir coefficients. I think the following ranges are correct? Does anyone know the conversion factor to get the coefficients to metric?

Broad Crested Weir C=2.6-3.1(imperial)
Sharp Crested Weir C=3.1-3.3(imperial)
Trapezoidal Weir C= 2.7-3.1 (imperial)
Cipoletti Weir C=???
Ogee Weir= 3.2-4.1 (imperial)

Thanks in advance.

 

[psmart]

Ryb01: Imperial coefficient = Metric coefficient * 1.81


Peter Smart
HydroCAD Software

http://www.hydrocad.net

 

[psmart]

I should have been more specific: 1.81 is the conversion factor for the traditional WEIR coefficient.

Peter Smart
HydroCAD Software

http://www.hydrocad.net

 

[Ryb01]

Thank you psmart!

 

[SMIAH]

You convert an imperial coefficient by using:

C(imperial) * (9.81/32.2)^0.5

So a C (Imperial) of 3.1 = 1.71 in metrics.

Broad Crested Weir C= 1.45 - 1.71
Sharp Crested Weir C= 1.71 - 1.83
Ogee Weir C= 1.83 - 2.26