Problem $3[10$ points$]$: A natural$-$draft cooling tower is to remove $70$ MW of waste heat from the cooling water that enters the tower at $\backslash (42^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and leaves at $\backslash (30^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Atmospheric air enters the tower at $1$ atm with dry$-$ and wet$-$bulb temperatures of $23$ and $\backslash (16^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ respectively, and leaves saturated at $\backslash (32^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Determine

$($a$)$ The mass flow rate of the cooling water,

$($b$)$ The volume flow rate of air into the cooling tower, and

$($c$)$ The mass flow rate of the required makeup water.