Question $5\mathrm{.}5$

A valley is $4km$ in width and $18km$ in length. The concentration of methane entering the valley is $1\mathrm{.}1m\frac{g}{m^3}.$ An inversion layer hangs over the town at a height of $130m.$ The wind at one$-$half the mixing height blows at $5\mathrm{.}1\frac{m}{s}$ into the valley. The degradation of methane in the atmosphere can be described by first order kinetics with a rate constant of $\frac{0\mathrm{.}000725}{h}r.1420$ hydraulic fracturing wells each release methane at a rate of $2\mathrm{.}5\frac{g}{s}.$ Methane is also released from the three confined animal feeding operations $($CAFOs$)$ in the valley. Each CAFO has an average of $1500$ cattle. Each cattle emits methane at a rate of $12\mathrm{.}2\frac{g}{h}r.$ Determine the steady$-$state concentration in $m\frac{g}{m^3}$

Inflow

$U=5.$

$C_{in}=1\mathrm{.}1$

Question $5\mathrm{.}7$

Refer to question $5\mathrm{.}5$ and answer the following questions:

a$)$ Draw a diagram showing the system and flow of methane into and out of the valley

b$)$ Write the general mass balance equation describing the fate and transport of methane in the valley

c$)$ State your assumptions in constructing the mass balance equation and determining the methane concentration

d$)$ If the hydraulic fracking wells suddenly ceased operation but the CAFOs still operated, determine the concentration $($in $m\frac{g}{m}3)$ of methane after $2$ days.