A rapid$-$sand filter treats $0\mathrm{.}2\frac{m^3}{s}$ of water. The filter bed contains $100$ percent $30-50$ U$.$S$.$ mesh sand. The sand bed has a depth of $0\mathrm{.}6$ m $,$ porosity of $0\mathrm{.}42,$ and a shape factor of $0\mathrm{.}9.$ The absolute viscosity and the density of water are $1\mathrm{.}139{10}^{-3}Pa-$s and $999k\frac{g}{m^3},$ respectively. At a filter loading rate of $200\frac{m^3}{d}-m^2,$ determine the head loss for each clean filter bed using the Rose equation.