$10($a$).$ Consider a tall stack emitting $P{M}_{2\mathrm{.}5}$ at the rate of $15\frac{g}{s}$ in the atmosphere where the wind is blowing in X$-$direction with an average velocity of $4\frac{m}{s}$ at the effective stack height. What will be the maximum ground level concentration in centerline if the Gaussian plume is assumed with dispersion parameters ${}_y=50m$ and ${}_z=30m?$ The physical stack height is $40m.(8$ marks$)$ The following equations may be used.

$C(x,y,z)=\frac{Q}{u_H{}_y{}_z}$exp$(\frac{-y^2}{2{}_y^2})exp(\frac{-H^2}{2{}_z^2})$

$h=\frac{v_{s}d}{u}[1\mathrm{.}5+(2\mathrm{.}68{10}^{-2}(P)(\frac{T_s-T_a}{T_s})d)]$

Q: source strength $($e$.$g$.,kg{s}^{-1})$;

$x$ : the distance downwind from the source;

$y$: the lateral distance from the mean wind direction;

$z$ : the height above ground level;

$H$:$h+h,$ the effective height of the release, $h$ is the physical height of the chimney;

$h$ : the additional height by which the plume rises due to its buoyancy and$/$or momentum; $u_H(u)$ : the mean wind speed at plume height;

${}_y$: horizontal dispersion coefficient $($standard deviation$),m$;

${}_z$: vertical dispersion coefficient $($standard deviation$),m$

Gas exit velocity: $v_s=5\mathrm{.}5\frac{m}{s}$;

Gas exit temperature $(K)$:$T_s=120C$;

Stack tip diameter $(m)$:$d=3m$;

Ambient temperature $(K)$:$T_a=20C$;

Atmospheric pressure $(kPa)$:$P=101\mathrm{.}3$kPa.