A catalyst having spherical particles of $D_p=50m$ and ${}_p=1650k\frac{g}{m^3}$ is to be used to contact a hydrocarbon vapor in a fluidized reactor at $485C$ and $1$atm. At rest the bed has a porosity of $0\mathrm{.}35$ and a height of $1m.$ At operating conditions, the fluid viscosity is $0\mathrm{.}02cP$ and its density is $3\mathrm{.}5k\frac{g}{m}3.$ Determine

a$)$ the superficial gas velocity to fluidize the bed;

b$)$ the velocity at which the bed would begin to be carried out with the gas.