Example $3$: A non$-$uniform stratified sand filter described in Table below is to be backwashed at

the velocity of $2\mathrm{.}5{10}^{-2}\frac{m}{s}.$ Determine the depth of the expanded bed for the sand filter using

the following assumptions:

The bed depth $=0\mathrm{.}65m$

Porosity $=0\mathrm{.}45$

Drag coefficient $=0\mathrm{.}4$

Shape factor $=0\mathrm{.}85.$

Density of water $=1000k\frac{g}{m^3}$

Viscosity $=1{10}^{-3}N.$sec $\frac{?}{m^2}$

SG of the filter particles $=2\mathrm{.}6.$