(Solved): 2. Water flows using gravity from an upper tank A to a lower tank B through two pipelines. One pip ...

2. Water flows using gravity from an upper tank A to a lower tank B through two pipelines. One pipeline is \( 800 \mathrm{~m} \) in length and has diameter \( 0.2 \mathrm{~m} \). The second pipeline is \( 700 \mathrm{~m} \) in length and has diameter of \( 0.15 \mathrm{~m} \). The heights of the water levels are different by \( 100 \mathrm{~m} \). If the two pipelines are replaced with a single pipeline that is \( 700 \mathrm{~m} \), then find (a) the diameter of the pipeline be that maintains the same flow rate as the two combined flow rates, in units of [m] (b) the flow rate in the single pipeline, in units of \( \left[\mathrm{m}^{3} / \mathrm{s}\right] \) (c) List any assumptions used in your solution