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Re: Modeling bridge piers
Mike Schmidt wote an article on this in SWMM News & Notes recently (Vol4 No 3).
You can use any bridge pier coefficients you can find in the literature; e.g., see Chow, Open channel Hydraulics, which summarizes the Carter- Kindswater experimental data. But again, you can use any that you can find as best fits your bridge. All of these results can be reduced to the form head loss DelH = k* Hv. The Carter-Kindswater data can be reduced to k=1/C^2, where C is the product of Ci,s for various geometric effects (Chow 1959, p 479).
The key to this is that you have a 1-D model and no matter the gyrations of the plan geometry, they can all be represented by one number "k". This applies to all the 1-d models, including Extran, HEC2, WSPRO, etc.
Then you substitute this k in the " equivalent n" formula and presto, you have an n value that fully incorporates the headloss coefficient you specified for the bridge piers and the bridge opening.
The equivalent n formula is as follows:
ne = Ae/Ap * ( (Re/Rp)^4/3*(Lp/Le)*np^2
+( Re^(4/3) * Sum(Kpi)/(29.2*Le))^.5
Subscripts are as follows:
p prototype conduit (or bridge in this instance)
e subscript - equivalent conduit properties
This formula is also useful for bashing area shock, which can happen in the case of a narrow opening culvert or bridge and a wide approach channel. Just substitute the the approach channel properties for Ae and Re but use Le=Lp. Then correct for Courant condition as a separate step or let the program do it). By using the same area as the approaching channel, there is no more area shock. You may be surprised how high the "n" values go, depending on the severity of your area ratio.
Another user adds: all methods are subject to question. Assume bridge opening is multiple culvert
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Linear Mode
