The fluidized bed with a diameter of $0\mathrm{.}5m$ contains $420kg$ solid particles. The average diameter, shape factor and the density of these solid particels were given as $0\mathrm{.}2mm,0\mathrm{.}81,$ and $1500k\frac{g}{m^3},$ respectively. In order to fluidize the system air at $25C$ temperature and $1$atm pressure was used. If the fluidization length was determined as $2m,$ calculate:

a$.$ Minimum fluidization void fraction

b$.$ Pressure drop for fluidization

c$.$ Minimum fluidization velocity