$3.$ Pump

A pump steadily delivers water through a hose terminated by a nozzle. The exit of the nozzle has a diameter of $0\mathrm{.}6$ cm and is located $10$ m above the pump inlet pipe, which has a diameter of $1\mathrm{.}2$ cm $.$ The pressure is equal to $1$ bar at both the inlet and exit, and the temperature is constant at $20$ C throughout. The magnitude of the power input required by the pump is $1\mathrm{.}5$ kW $,$ and the acceleration of gravity is $\backslash (\backslash$mathrm$\{$g$\}=9\mathrm{.}81\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}^\{\backslash$wedge$\}2\backslash ).$ Determine the mass flow rate delivered by the pump, in $\backslash (\backslash$mathrm$\{$kg$\}/\backslash$mathrm$\{$s$\}\backslash ).$

Hint: the answer is $\backslash (1\mathrm{.}3254\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ).$