Acasta
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Actually this is the correct formula no matter what size pipe you use the problem is accounting for the pressure loss. For this problem the pressure loss in question is going to be the frictional loss in the pipe. In a 6mm ID pipe I would imagine there will be some fairly large pressure loss particularly over 16m.
Having said that you can't make the assumption that the flow rate of the open tap will be the same as that once 16m of 6mm ID pipe is attached to it. The increase in static pressure from the pipe will reduce the flow rate.
Yeah i know, the formula is correct, but on this scale its not really relevant. Your right, the friction in the pipe would be the main flow changer. And also the pressure at tap i have no idea how to get tap pressure, just taking a quick stab.