Solve the mass balance equation for fixed box model under unsteady$-$state conditions.

$\frac{dC}{dt}=\frac{u}{L}b-\frac{u}{L}C+\frac{q}{H}$

A factory in a rural area produces fermentation products with a capacity of $1000$ tonnes$/$yr$.$ The controlled

emission factor for odor emissions averages $20000$ odor units $($OU$)$ per kilogram of products, and all

emissions are released to the atmosphere through an elevated stack with an inner diameter of $0\mathrm{.}6m$ at the

point of release. The stack height is $50m.$ The flue gas is $15000N\frac{m^3}{h}.$ The stack gas temperature is $40C.$

a$)$ Estimate the ground level odor concentration $500m$ south of the factory if the wind blows from north

at a speed of $1\mathrm{.}5\frac{m}{s}$ on a sunny midday of July. Ambient temperature is $30C.$

b$)$ Estimate the ground level odor concentration $2km$ west of the factory if the wind blows from east

northeast $($ENE$)$ at a speed of $1\mathrm{.}1\frac{m}{s}$ on a clear sunrise of December. Ambient temperature is $2C$

Use Briggs formulae for estimating plume rise