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I am not aware of any programmes available specifically for designing gravity water systems. The design process is quite simple and can easily be accomplished using pencil and paper or an excel spread sheet. The pressure drop in simple branched systems can be designed using the Hazen Williams formula, or more easily using head loss charts such as the Hydraulics research Station Charts for the hydraulic design of channels and pipes (not available in electronic format). If you need a calculation programme to document your design then you could try Mathcad, avaialable for free at https://www.ptc.com/engineering-math-software/mathcad/free-download, but you will not require any advanced mathematics capabilities or algorithms to achieve an efficient design.

An overview of the design process can be found at https://www.ircwash.org/sites/default/files/221-82GR-1479.pdf

Drawing of the hydraulic profile is a relatively trivial task, and can easily be accomplished with a rule and some graph paper. IF you wish to use a CAD programme you can download Draftsight for free at https://www.3ds.com/products-services/draftsight-cad-software/free-download/.