Design a co$-$current adiabatic tunnel dryer to handle $2000$ kg$/$hr of wet sand from a

moisture content of $1$ to $0\mathrm{.}1$ kg water$/$kg dry sand. The equilibrium moisture content

for the sand is negligible.

The air available for drying has wet and dry bulb temperatures of $34\backslash$deg C and $93\backslash$deg C

respectively. The air leaves the dryer at $38\backslash$deg C and the solid leaves at $34\backslash$deg C$.$ A series

of preliminary tests under design conditions showed that the critical moisture

content of the sand was $0\mathrm{.}5$ kg water$/$kg dry sand and that the rate of drying above

this value was $1\mathrm{.}0$ kg water$/$m$2$

$.$hr$.$ Below the critical moisture content, the drying

rate fell linearly to zero at zero moisture content.

If the effective area of drying is $0\mathrm{.}3$ m$2$

$/$kg dry solid and, neglecting shrinkage,

calculate the length of dryer required if $20$ kg of dry material per m length is held.