At first glance, this Kindsvater paper would seem to address your concern directly:

http://pubs.usgs.gov/wsp/1617a/report.pdf

Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East - http://www.campbellcivil.com

Also note that different weir equations include different terms in their coefficients, resulting in different coefficient values being used for each equation. For example:

Rectangular Weir: C = 2/3 sqrt(2g) Cd (e.g. 3.26)

V-notch or Custom Weir: Cv = 8/15 sqrt(2g) Cd (e.g. 2.61)

Where g is the gravitational constant, and Cd is the unit-less discharge coefficient, which is typically 0.61, giving the typical C values shown above.

Note that the v-notch weir coefficient (which is also used for a custom weir in HydroCAD) is 80% of the rectangular weir coefficient. So you need to be careful when using a custom coefficient.

Peter Smart
HydroCAD Software
www.hydrocad.net

When considering a custom coefficient, also be sure to do a sensitivity study to determine how accurate you really need to be. For example, how much difference is there in the peak flow and WSE as you increase the weir coefficient from 2.6, to 2.8, or 3.0? In many cases the effect is minimal, suggesting that less precision is required in the choice of C value.

Peter Smart
HydroCAD Software
www.hydrocad.net