A fan is listed as having the following performance with standard air: Volume

discharge, $120$ m$3$

$/$s; Speed, $420$ rpm; Static pressure, $310$ mm water gage; and Brake

power, $620$ kW$.$ The system duct will remain the same and the fan will discharge the same

volume of $120$ m$3$

$/$s of air at $94$ oC and a barometric pressure of $735$ mm Hg when its speed

is $420$ rpm$.$ Find the brake power input and the static pressure required?