Air is moving upward in a bed packed with solid spheres in a column $($open to atmosphere$)$ with a cross$-$ sectional area of $0\mathrm{.}01$ m$2$ and a length of $1$ m$.$ The mass of the particles is $5$ kg$.$ The volume mean diameter of the particles is $50$ micron, and the density of the particles is $2500$ kg$/$m$3.$ Density of air $=1\mathrm{.}2$ kg$/$m$3.$ Viscosity of air $=1\mathrm{.}8\backslash$times $10-5$ Pa$$s$.$ The voidage of the packed bed of the spheres is $0\mathrm{.}4.$ At minimum fluidisation, the voidage of the packed bed of the plastic spheres is $10\%$ higher than that of the packed bed.

Answer the following questions:

a$)$ What is the depth of the packed bed?

b$)$ What is the minimum depth of the fluidised bed?

c$)$ Find the minimum and maximum superficial velocities of air for fluidisation while keeping ALL the particles within the column.