Epanet
Have a look at Epanet and the plugins for it in QGIS.
http://epanet.de/ghydraulics/index.html.en
https://plugins.qgis.org/plugins/ghydraulic/
and there is another epanet connector in the Plugins Manager menu which I haven't had any experience with.
Whilst Epanet is for pressurised pipelines and it deals with different anaylsis to your interests, it deals with a lot of the same concepts.
For instance in GIS a point/node does not natively have an orientation and so GHydraulics deals with this (afaik) by using very small lines as nodes.
General Method
Just some notes
- Whilst the DEM will be useful, it is hard for us to evaluate it without more information. Is the topography (i.e. the DEM) a rigorous indicator of the invert of sewer pipes or does the sewer line traverse ridges and gullies?
to what resolution is the aerial image? Does it show a scar on the landscape of the buried sewer line or more likely the paving and landscape obscure the pipe alignment. Do you have to plot other services like roads?
I'd be surprised if there is all this ancillary data available that there is not some existing schematic of the sewer alignment which shows direction of flow etc.
Unless you want to create an entirely theoretical model, some real flow and elevation data would be important for your work to have value to most end users. I can imagine excavating to the surface of a sample of pipes and taking elevation measurements. There are a range of technologies for sampling flows in pipes and providing estimates of the loadings.