Calculating additional velocity due to gradient

I've been looking into this an I think that the Manning equation is probably the option that I should use. Would anyone be able to confirm this please?

v = k_n/n R^2/3 S^1/2

Manning's Equation is one appropriate method to compute the velocity of flowing water. The slope should be in (ft/ft) or (m/m) and should represent the longitudinal slope of the conveyance structure you are evaluating. There are numerous books with roughness coefficients that you can use to get your roughness from and the "R" is hydraulic radius (Area/wetted -perimeter). You did not provide enough information, however. What velocity are you seeking the velocity on the bridge or under the bridge? Forgive my misunderstanding; but, what is a spitterpipe?

gbam,
Thank you very much for your reply. I purposely didn't include all of the information as I believe certain factors weren't required for my query. I can see now that you may have thought that the structure possibly spanned over water, it doesn't.
The velocity that I was seeking for was the storm water passing across the surface of the footbridge due to the increase in elevation at one end.
To answer your final question, a spitter pipe is essentially a pipe to discharge water. Please see attachment.
MDBris

Thanks for the clarification of a spitter pipe.

What flow rate are you using to compute the velocity? Was that computed using rainfall runoff processes?

Oh, I should clarify that the slope used in Manning's Equation is the slope of the Energy Grade; however, for normal flow the slope would be the slope of the channel.