$($Filtration$-50$ points$)$ Calculate the initial head loss through a dual$-$media filter consisting of a $12-$in$.$ layer of uniform anthracite with a grain diameter of $2\mathrm{.}0$ mm and a $24-$in$.$ layer of uniform sand with a grain diameter of $1\mathrm{.}0$ mm at a filtration rate of $4\mathrm{.}0gp\frac{m}{f}{t}^2.$ The porosity of both media is $0\mathrm{.}40,$ the shape factor for the anthracite is $7\mathrm{.}5,$ and the shape factor for the sand is $6\mathrm{.}0.$ Assume a water temperature of $60F.($Hint: first calculate filtration rate in each medium in $f\frac{t}{s}$ and then calculate total head loss through a dual$-$media filter as sum up head loss in anthracite and sand layers, Kozeny equation$)$