why water become thinner when falling?
Because it becomes faster whereas the volumetric flow rate remains constant.
why volumetric flow rate is constant?
Why should it change, if you don't touch the handles?
"Volumetric flow" is the amount of water coming out of the faucet in a given time. That does not change. But as the water falls, its acceleration is, of course, g so that its speed is constantly increasing.
if water fall from a large height what happen?(molecules very close to each other)
You can see it in your sink or a waterfall: the water separates into droplets due to surface tension.
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