$5-74$ A fan is to be selected to ventilate a bathroom whose dimensions are $\backslash (2\backslash$mathrm$\{$~m$\}\backslash$times $3\backslash$mathrm$\{$~m$\}\backslash$times $3\backslash$mathrm$\{$~m$\}\backslash ).$ The air velocity is not to exceed $\backslash (7\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ to minimize vibration and noise. The combined efficiency of the fan$-$motor unit to be used can be taken to be $50$ percent. If the fan is to replace the entire volume of air in $15$ min, determine $(\backslash ($ a $\backslash ))$ the wattage of the fan$-$motor unit to be purchased, $\backslash (($b$)\backslash )$ the diameter of the fan casing, and $\backslash (($c$)\backslash )$ the pressure difference across the fan. Take the air density to be $\backslash (1\mathrm{.}25\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash )$ and disregard the effect of the kinetic energy correction factors.

FIGURE P$5-74$