What is the intended use of this information (if it is for determining how much pipe to restrain from pressure thrust at various thrust foci, DIPRA provides recommendations for this at e.g.
A lot of pipe specs I see for smooth outside pipes limit the maximum slope to 10%. I'd go with a corrugated outside pipe steeper than 10%. Then you could get back to soil to soil friction as the soil fills the corrugations.
You'll need to consider hydraulic issues with pipes sloped more than 10%. Maybe thrust blocks on every joint.
You never said why you are needing the info. What's the application?