Problem $1$: The duct system below is required to deliver air to three spaces as shown in the figure. Size the various sections of the system using the equal$-$friction method and round duct. Use the nearest whole size duct $($odd or even$).$ A total pressure of $0\mathrm{.}13in.wg$ is available at the plenum. There is a $90$ deg round to rectangular boot at the end of each run in addition to the diffuser loss given in the figure.

$($a$)$ Assuming a $$ Po of $0\mathrm{.}1$ in $w\frac{g}{100}ft$ size the ducts for each section

$($b$)$ By section, list the losses in each section, give the Le$/$D for each loss in that section, and the total equivalent length for that section.

$($c$)$ Compute the $$ Po for each section.

$($d$)$ Compute the $$ Po for each run.

$($e$)$ Is this system balanced? If not, what needs to be done to balance the system?