One of your first tasks is to evaluate the ore crushing and roasting process. You are

given the following information and guidelines:

The feed rate to the crusher is $2$ tonnes per hour, and the characteristic size

of the ore entering it is $50mm.$ The crusher is driven by an electric motor and

the cost of electricity is $$0\mathrm{.}18$ per $kWh.$

The specific energy requirement is given by Kick's Law; the value of $C_K$ for the

ore is $16kJk{g}^{-1}.$

In your calculations you can assume that all the ore entering the crusher

leaves it and enters the fluidized bed roaster; all the particles in the fluidized

bed have the same mean size as those entering it from the crusher.

Product is continuously withdrawn from the fluidized bed which operates at a

steady state. The diameter of the fluidized bed is $1\mathrm{.}75m$ and the operating

superficial velocity is $3U_{mf}.$ At operating conditions, the density and viscosity

of the fluidizing gas are $0\mathrm{.}3kg{m}^{-3}$ and $4590{10}^{-8}kg{m}^{-1}{s}^{-1}$ respectively; the

density of the ore is $2400kg{m}^{-3}.$

All the fluidizing gas enters the cyclone; there are no heat losses from the

ducting and no leaks. The velocity of the gas in the rectangular cyclone entry

port is $18m{s}^{-1}$ and the diameter of the cyclone, $D,$ is $2\mathrm{.}0m.$

The dimensions of the cyclone relative to its diameter, $D,$ are given in Figure

$4\mathrm{.}1$ below.

If the crusher runs for $8,000$ hours per year, calculate the annual cost of running it$.$

Show and explain all your working and justify any assumptions you make.