A closed$-$loop solid recirculation system, as shown in Fig. $7,$ contains a bed

of solids at the bottom of a $20\mathrm{.}3-$cm ID tube $8$ m high, which is thought to

be higher than the TDH$.$ In a typical experiment the bed is charged with

$8$ kg of coarse nonentraining solids, $1$kg of $50-\backslash$mu $,$ m solids, and $1$kg of

$100-\backslash$mu $,$m solids. At steady state, carryover is $0\mathrm{.}03$ kg$/$s$,$ and $1$kg of solids

are present in the recycle loop at any time. A sample of the entrained

solids shows that it consists of two parts $50-\backslash$mu m particles to one part of

$100-\backslash$mu m particles. From this information find $\backslash$kappa and $\backslash$kappa $*$ for these two sizes

of elutriable particles.