Water is flowing through a $0\mathrm{.}05$ m diameter pipe from a large reservoir, as shown. The water level in the reservoir is $35$ m above the horizontal pipe segment at the exit from the tank. The pipe initially is bent down and later up$,$ emerging above the ground level. The

loss coefficient in the three elbows is $K=0\mathrm{.}25,$ and we can assume a Darcy friction coefficient of $f=0\mathrm{.}02.$ Also for water $=1000k\frac{g}{m^3}$;$={10}^{-3}N\frac{s}{m^2}.$

$($a$)(10\%)$ If the maximum height of the jet is $h=0\mathrm{.}5m,$ calculate the exit velocity at ground level, the Reynolds number and the flow rate $Q.$

$($b$)(15\%)$ Calculate the total length of the pipeline.

Note: this problem is different than the one in the homework

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