Alumina powder is fed into a pipe with a diameter of $5\mathrm{.}5$ in and $12$ in high until the thickness is $10$ in$.$ alumina bulk density $64$ lb$/$ft$3.$ Air is injected into the pipe from the bottom to fluidize the alumina. fluidize the alumina. The air flow velocity is $158$ lb$/$Jft$2.$ Alumina grains are $0\mathrm{.}0042$ in$.$ physical properties: a Air Specific heat $=0\mathrm{.}25$ BTU$/$lbF Meeting $=0\mathrm{.}074$ lb$/$cuft Viscosity $=0\mathrm{.}0435$ lb$/$Jft b Alumina grain Specific heat $=0\mathrm{.}19$ BTU$/$lbF Meeting $=16\mathrm{.}7$ lb$/$cuft Calculate:

a$.$ Minimum fluidization speed

b$.$ Bed development after fluidization