$(20$ Points$)$ Calculate the initial head loss $($in meter$)$ through a dual$-$media filter consisting of a $0\mathrm{.}40-m$ layer of uniform anthracite with a grain diameter of $1\mathrm{.}0$ mm and a $0\mathrm{.}20-m$ layer of uniform sand with a grain diameter of $0\mathrm{.}50$ mm at a filtration rate of $3\frac{L}{s}\frac{?}{m^2}.$ The porosity of both media is $0\mathrm{.}42,$ 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 $15C.$