$(x,y,0,H)=\frac{E}{s_y{s}_{z}u}$exp$[-\frac{1}{2}(\frac{y}{s_y}{)}^2]exp[-\frac{1}{2}(\frac{H}{s_z}{)}^2]$

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

Figure Q$4($a$)$ The emission of $S{O}_2$ from a coal$-$fired power plant is $2000\frac{g}{s}$ as shown in Figure Q$4.$

If the wind speed at top of the stack is $3\frac{m}{s}.$ By using the "Basic Point Source

Gaussian Dispersion Model",

$($i$)$ Evaluate the effective height of the stack.

$(2$ marks$)$

$($ii$)$ Evaluate the value of $S_y$ and $S_z$ for position point $P.$

$($iii$)$ Calculate the concentration of the $S{O}_2$ at the ground level point $P.$

$($iv$)$ If point $P$ is moved to $P^{\text{'}},$ what is the concentration of $S{O}_2$ at point $P\text{'}?$

Parameters:

atmosphere pressure at the exit $=95$kPa

atmosphere temperature $=25C$

stack height $=120m$

stack diameter $=1\mathrm{.}5m$

stack exit temperature $=350C$

stack exit velocity $=15\frac{m}{s}$

$S_y=250(x{)}^{0\mathrm{.}894}$

$S_z=44\mathrm{.}5(x{)}^{0\mathrm{.}516}-13$