Example #$2$ : Determination of headloss across a bed of nonuniform particles

Water at $20C$ is passed through a filter bed at $4\mathrm{.}32\frac{m}{h}r.$ The bed is $0\mathrm{.}75m$ deep and is composed of nonuniform sand $($sp$.$ gravity$=2\mathrm{.}65)$ stratified so that the smallest particles are on top, the largest on bottom. The porosity and shape factors are $0\mathrm{.}4$ and $0\mathrm{.}85$ throughout the depth of bed. The size distribution of the granules given in the table below. Determine the headloss for clean water flow through bed.

at $20C$;$=1\mathrm{.}002{10}^{-3}k\frac{g}{m}.sec,=998\mathrm{.}2k\frac{g}{m^3}$

Sieve Analysis Results:

$\backslash$table$[[$U$.$S Sieve No$.,\backslash$table$[[$Particle Size range,$],[$mm$]],\backslash$table$[[$Weight$],[$fraction$],[$retained$,x_{ij}$