$5-80$ Water is pumped from a lower reservoir to a higher reservoir by a pump that provides $23$ kW of useful mechanical power to the water. The free surface of the upper reservoir is $57$ m higher than the surface of the lower reservoir. If the flow rate of water is measured to be $\backslash (0\mathrm{.}03\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ),$ determine the irreversible head loss of the system and the lost mechanical power during this process.

FIGURE P$5-80$