The fluidized bed is operated so that it is maintained at a superficial velocity, $U,$

such that $U=K_s{U}_{mf}$ where $K_s$ is a constant multiplier, and $U_{mf}$ is the minimum

fluidizing velocity. $K_S$ is maintained at a constant value by adjusting the flow

rate of the fluidizing air so that the pressure drop across the distributor plate

has the value predicted by theoretical equations used to design it $($see below$)$

when $U=Ks{U}_{mf}.$

The density of powder $S$ is $2500kg{m}^{-3},$ and a sieve analysis for it is given in

Table $6\mathrm{.}1.$Table $6\mathrm{.}1.$ Sieve analysis of sample of powder S$.$

At the operating conditions of the fluidized bed the density of the fluidizing gas

is $1\mathrm{.}127kg{m}^{-3}$ and its viscosity is $1912{10}^{-8}kg{m}^{-1}{s}^{-1}.$

The diameter of the fluidized bed is $0\mathrm{.}5m$ and the diameter of the distributor

plate is the same. The distributor has $26$ orifices each $2mm$ in diameter.

The pressure drop across the distributor at operating conditions is $2417\mathrm{.}6Pa.$

Calculate $Ks.$