HEC's "GeoRas 's 10" ArcGIS extension link is http://www.hec.usace.army.mil/software/hec-georas/. Best used with HEC's "HEC-RAS" program link is http://www.hec.usace.army.mil/software/hec-ras/
I believe there is a "gridding" extension that will convert a 3D vector file to an ArcGIS grid. I can't remember the name of the extension, but may be someone else can provide it.
I assumed you had a shape file. A 3D contour mapping would have the elevation in the ".shp" file. I believe the conversion requires both the Spatial Analysis and 3D Analysis extensions. I hope this clears up my comment.
I believe that you need first configuring a network with active nodes in your shapefile and then using Hec- GeoRAS or assess the utilities of ArsGis for hydrological analysis (basic functions).
There is a tool. You can use spatial analysis tool and use arc hydro which incorporated now if using 10.0, 10.1, or 10.2. You can use flow direction tool, flow accumulation
Your best option is HEC-RAS version that works with ArcGIS. Other option is ArcHydro. But if you are focusing on open channel hydraulics, then you might want to use HEC-RAS, it has a lot of tools that will make your life easy. You can specify streams, rivers, cross-sections, bridges, elevations and so on. If you want to bring in the effect of surface runoff, that may be a little bit of a challenge.
You can set different values of Manning for the different zones of each cross section of your model. You will get water levels and velocities for each cross section. You can then export your results in arcmap using HEC GEO-RAS, obtaining rasters with the distribution of water levels and velocities throughout the whole channel.
If you have problems in using ArcGIS and want to try and open source alternative, you could probably have a look at this guide for "Estimating a Base Flood Elevation using QGIS": http://wvfma.org/wp-content/uploads/2013/05/Estimating-a-BFE-with-Quantum-GIS.pdf