Hypothetically, let's assume the USF administration is considering building a coal$-$fired steam plant on the USF campus to alleviate the rising costs of purchased electricity. You have been asked to help with an assessment of the impact of the proposed plant pollutant plume on the residences.

Information about the proposed plant you obtain includes that the SO$2$ emission rate will be $7\mathrm{.}1$ tonnes$/$day$,$ the stack height will be $50$ m$,$ stack inside diameter will be $2\mathrm{.}5$ m$,$ and vertical stack exit velocity and exit temperature are expected to be about $30$ m$/$s and $470$ K$,$ respectively.$$ You will study a typical day with the sun shining brightly, a wind speed of $4$ m$/$sec $($measured at a height of $10$ m$),$ ambient temperature of $28$ C$,$ and pressure of $1$ atm.$$ Assume the wind is flowing from west to east, and the residences are $0\mathrm{.}6$ km to the east and $30$ m south of the plant.$$

$($a$)$ Determine which stability class you will be assuming here.

$($b$)$ Estimate the effective stack height for these conditions.$$ Use the Holland Formula $($with multiplier, if applicable$)$ for simplicity.$$

$($c$)$ Write down the Gaussian plume equation you will be using to estimate conservative concentrations at the residences. $$Due to the short distance between the proposed plant to the receptor location and typically high inversion heights, you will not consider the effects of an inversion on concentrations $($but should consider effects of the ground$).$

$($d$)$ Clearly list the values $($including units$)$ you will use for each of the terms appearing in your concentration equation.

$($e$)$ Calculate the SO$2$ concentration at the residence building both at the ground level and at the third floor $($elevation of $20$m$).$

$($f$)$ Compare these values to the National Ambient Air Quality Standards $($NAAQS$)$ for SO$2.$ Discuss whether the students on the third floor should demand that they are moved to the first floor? $($Consider uncertainties assumptions, input parameters, and equation.$)$

$($g$)$ Calculate and plot the concentration as a function of receptor altitude $($on an altitude versus concentration graph$)$ at plume centerline and a downwind distance of $600$m$.$You will want to do this with using excel, Matlab, or R $($or by hand with graph paper, but that is tedious$).$ Discuss what you see.

$($h$)$ Now calculate and plot the concentration as a function of downwind distance at plume centerline and ground level.$$ Use a separate graph.$$

In the following questions, do not do calculations.$$ Instead, look at the original equation and discuss expected effects on the location and intensity of the peak, amount of spread, etc.$$ Draw, by hand, the expected concentration profiles with vertical and downwind distance, compared to the standard case, and discuss your logic. $($You are encouraged to do the calculations afterward, to confirm or refute your intuition.$)$

$($i$)$ If the windspeed were to increased, leaving the stability class unchanged, how would the concentrations change relative to the standard case? $$How would concentration profiles change?$$

$($j$)$ Suppose, instead of daytime it was a cloudy night.$$ How would concentration profiles change?$$

$($k$)$ Suppose, instead the effective stack height was increased.$$ How would concentration profiles change?