A utility worker is fixing power lines in a manhole space at a busy intersection as shown below. A major portion of car exhaust is carbon dioxide $(C{O}_2).$ The density of air at standard conditions is lower than $C{O}_2,$ therefore, $C{O}_2$ will tend to settle into the bottom of the manhole space and displace the oxygen, posing a very relevant danger of suffocation to utility workers. To avoid suffocation, a fan is used to supply fresh air from the surface into the manhole space as shown in below. The air is routed through an $8-$in$.-$diameter plastic hose that is $30$ ft in length. Determine the horsepower needed by the fan to overcome the head loss with a required flowrate of $600f\frac{t^3}{m}in$ or cfm $,$ when $($a$)$ neglecting minor losses and $($b$)$ including minor losses for one sharp$-$edged entrance, one exit, and one $90$ miter bend $($no guide vanes$).($c$)$ Show that $C{O}_2$ indeed is denser than air. To estimate density of air and CO $2,$ you can consider atmospheric temperature of $70F.$ You can also consider the effect of change of elevation is not significant $($why$?).$

$($c$)$ TIM MCCAIG$/$iStockphoto$.$