Suppose you build a rural house, where you need to run a pipe to the nearest water supply, which fortunately is about 1 Km above the elevation of your house. The gage pressure at water supply is 1 Mpa and the pipe length will be about6 Km. You require a minimum of 3 gal/min when you your end of the pipe is open to the atmosphere. To minimize cost, you want to buy the smallest possible diameter pipe.
(a) plot the pressure loss from pipe inlet to exit, neglecting minor losses, as a function of roughness for various pipe materials.
(b) which is more important to this problem, the loss due to elevation difference, or the loss due to the pressure drop in the pipe?
(c) your family grows over time and the required water supply grows beyond the 3gal/min Plot the required pipe diameter as a function of water supply requirement, now assume that the pipe is a very smooth one.