$(20$ pts$)$ A multimedia filter bed is designed to have $3m$ anthracite, $1m$ sand, and $1\mathrm{.}5m$

garnet with $0\mathrm{.}6m$ underdrain under $4m$ of water. Assuming pipes are designed for water

velocity of $4\frac{m}{s},$ what is the head loss through the system if the relative pressure at the

effluent is zero?