Air enters a fan through a duct at a velocity of $6\mathrm{.}5$ m$/$s and an inlet static pressure

of $2\mathrm{.}5$ cm H$2$O less than atmospheric pressure. The air leaves the fan through a duct at a

velocity of $11\mathrm{.}5$ m$/$s and a discharge static pressure of $7\mathrm{.}62$ cm H$2$O above the atmospheric

pressure. If the specific weight of air is $1\mathrm{.}20$ kg$/$m$3$ and the fan delivers $9\mathrm{.}45$ m$3$

$/$s$,$ determine

the fan theoretical power and the fan efficiency when the power input to the fan is $13\mathrm{.}75$ kW

at the coupling?