$5\mathrm{.}21$ Water from a hydrant passes through $450$ m of $60$ mm pipe and is discharged from a nozzle at the same height as the hydrant. Pressure head at the hydrant is $45$ m of water. If the friction factor $f$ for pipe is $0\mathrm{.}02$ and $C_v$ for the nozzle is $0\mathrm{.}96,$ find the diameter of the jet producing maximum jet momentum and the corresponding velocity of the jet.

Ans. $,17\mathrm{.}5mm$;$20\mathrm{.}17\frac{m}{s}.$