Sponge iron is being produced in fluidized bed reactor by reducing fing particles of $F{e}_2{O}_3($average particle size $=0\mathrm{.}5mm)$ at $1000K$ by a reducing gas. The gas consists of $50$ volume percent $H_2$ and $50$ volume percent $CO$ and its viscositip is $2{10}^{-5}kg{m}^{-1}{s}^{-1},$

Calculate: $($a$)$ Critical pressure drop per metre height of the bed at the onset of