The solid particles with $0\mathrm{.}1mm$ dimension and $0\mathrm{.}86$ shape factor were used in fluidized bed as packing material. The density of the solid particles was given as $1200k\frac{g}{m^3}.$ Air at $25C$ temperature and $202\mathrm{.}65$kPa pressure was used as the fluidization fluid. Moreover, minimum fluidization void fraction, diameter of the bed and weight of solid particles were given as $0\mathrm{.}43,0\mathrm{.}6m$ and $350kg,$ respectively. Calculate;

a$.$ Minimum fluidization length of the bed,

b$.$ Pressure drop for fluidization

c$.$Minimum fluidization velocity

d$.$Deetermine the void fraction when the system has a velocity $4$ times greater than minimum fluidization velocity.