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The actual flow out of each switch's outlet depends on that branch's pressure, which in turn is based off some poorly understood equation and the smallest pipe in the path. The path with all big pipes gets the large pipe's multiple applied to its pressure, while the path with medium and large pipes gets the medium pipe's smaller multiple applied to its pressure, much like with pressure gained/lost with elevation.
I've done some testing: connected 3 small water towers to one side of a big tower via switch using only big pipes, while on the other side of the same tower I made a similar configuration, but using one big pipe into three medium ones.
Logic suggests that there should be no difference in total water flow, since three medium pipes combined can move greater volume of water than a singular big one, yet somehow the side with three big pipes not only has higher pressure, thus delivering more water, but also goes over the maximum throughput of a large pipe by about 100 m³.
If you want, though I am kind of taking a break from water stuff.
I am sure you can understand why.
Sewage pipes just need to connect a higher building outlet to a lower building inlet for maximum sewage flow, but high water flow requires high pressure. A 10m drop will only add about 15 m³/day of flow with a large pipe, so if you are fine with small flow amounts through the largest (most expensive) pipes, you can get away without using pumps and storages on mostly flat areas.
"Otherwise if your output position is less in height than input source, you don't need to pump"
Generally yes, but the internal storage height of these buildings may change this. For example, water will not flow from a well to a water treatment plant even with a 10m drop, and you'll be getting almost no flow with a 15m drop.
pump water well to storage
pump sewage to outlet
Otherwise if your output position is less in height than input source, you don't need to pump
Is this true? Do I understand correctly