A settling chamber that is $12$ m long, $2$ m high, and $2$ m wide processes $240$ m$^3/$m of air at a temperature of $75\backslash$deg C$.$ Determine the maximum size of the particle with specific gravity of $1\mathrm{.}8$ that is removed with a theoretical efficiency of $100$ percent.

remember the shape here is cylindrical not rectangular $.$

use the following equations Equation $9-1$: $\frac{v_t}{H}=\frac{v_h}{L}$

$v_t$ : Terminal settling velocity, which is the constant speed at which a particle settles in a fluid.

$H$ : Height of the settling chamber, measured in meters $($m$).$

$v_h$ : Horizontal flow$-$through velocity, which is the speed of the gas flow moving horizontally

through the chamber, measured in meters per second $(\frac{m}{s}).$

$L$ : Length of the settling chamber, measured in meters $(m).$

Derived equation: $v_t=\frac{v_{h}H}{L}$

This equation is derived by solving for $v_t$ from Equation $9-1.$

Substitution into Eq$.(7-3)$: $\frac{v_{h}H}{L}=\frac{g({}_p-{}_a)d_p^2}{18}$