Discharge Coefficient
Discharge Coefficient
(OP)
I am curious to know which method/technique/equation or what degree of complexity everyone use to determine the coefficient of discharge C in the relation Q = CLH^3/2. This for, let's say, a broad-crested weir.
Keeping in mind that most of the larger dams have a complex geometry, and therefore physical models have been used extensively.
Keeping in mind that most of the larger dams have a complex geometry, and therefore physical models have been used extensively.





RE: Discharge Coefficient
For design, we usually balance conservative assumptions (low C value and thus wider and deeper spillway) with a desire to accurately estimate the actual flow depth and rate (perhaps higher c values and more actual capacity in the spillway).
For a service spillway, you may want to go with a physical model. For an emergency spillway, go with conservative design. For a large dam, always go with a physical model if you can convince your client to spend the money.
RE: Discharge Coefficient
Peter Smart
HydroCAD Software
www.hydrocad.net
RE: Discharge Coefficient
RE: Discharge Coefficient
Suppose you have a broad-crested rectangular weir with no end contractions and no submergence effects (not a creager/ogee spape spillway).
The discharge coefficient over a broad-crested weir shouldn't be higher than 1.7 in Metric or 3.08 in English.
Some suggest that C should be around 1.1 (2.0 in English), when some others suggest a value of 1.45 (2.63 in English).
What equations do you use?
RE: Discharge Coefficient
RE: Discharge Coefficient
The weir is nothing more than a combination of the energy equation and Froude equation. If you were to derive it, you'd find that C is a function of only the Froude number and gravity. Hence, the weir equation represents the energy of rectangular flow Q with some Froude F. Assuming critical flow fully develops (F = 1) then C = 3.1 (US). For some silly reason long ago engineers started using the C as an empirical catch all variable. When in fact the H is the real variable. Understanding this, you can avoid using C vs. H tables, which are nothing more than conversions between using H as the variable and using C as the variable.
The tricky part is determining the head losses between the point of reference to where critical flow develops. This varies greatly on the type of spillway and entrance conditions.
RE: Discharge Coefficient
2.63 is approximately equal to values that we have used for design of trapezoidally shaped emergency spillways. This is a generally very conservative value assuming there is free flow in the spillway channel. Again, this is a conservative number useful for design, maybe not so useful for estimating actual flow depths. Actual value will vary with depth of flow, approach conditions and geometry. See Brater and King, chapter 5 Q=CLH^3/2 and table 5-3 lists values for C ranging from 2.63 to 3.32. 2.63 is the lowest value listed in the table.
RE: Discharge Coefficient
(3rd edition, 1939).
RE: Discharge Coefficient
If you're trying to estimate flow rates based on observed head, you would want a more accurate value. But some calculations (such as a hydrograph routing through a pond) can be relatively insensitive to the exact weir coefficient. This is easy to verify by trying a couple of values.
Peter Smart
HydroCAD Software
www.hydrocad.net
RE: Discharge Coefficient
I've back calculated C values from spillway results using standard step methods (NRCS Sites, and HEC-RAS) and found C can be as low as 0.5 (US) for the first foot or so of head, increasing to and leveling off at about 2.6 (US) for 5 feet of head.
But I digress to my first comment that at the point where critical flow develops, C = 3.1 and H = [reservoir head] - [energy losses in the channel].
RE: Discharge Coefficient
I have it here and I must say it looks pretty brilliant.
Indeed, it might be too much to check for the exact weir coefficient, but I don't like using C=1.45 blindly as HEC RAS sometimes makes me do.
RE: Discharge Coefficient
Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East - http://www.campbellcivil.com
RE: Discharge Coefficient
This is very interesting as I usually design with a C that is higher than 0.5 for the first foot or two. I guess that I should specify a lower C for such conditions to be more conservative.
RE: Discharge Coefficient
RE: Discharge Coefficient
Going back to my original example of a vegetated spillway. If the point of reference is the downstream end of the level section, then: C = 3.09 and H = [Stage] - [Losses]. If the reference point is the upstream end, then C = f(F,g) and H = Stage.
Determining the upstream Froude (F) in a vegetated spillway is a topic for another post.
RE: Discharge Coefficient
RE: Discharge Coefficient