$9.$ Packed Bed Dynamics: A packed bed reactor with a diameter of $1$ m contains a liquid$-$solid flow. If the pressure drop across the bed is $500$ Pa$/$m and the solid particle diameter is $5$ mm$,$ estimate the liquid velocity.

$10.$ Fluidized Bed Operation: Calculate the minimum fluidization velocity for a fluidized bed containing particles of $100$ m diameter and density $2500$ kg$/$m$,$ with air as the fluidizing medium at $20$C and $1$ atm pressure.

$11.$ Pneumatic Conveying: For a pneumatic conveying system carrying solid particles at a velocity of $15$ m$/$s in a $100$ mm diameter pipe, calculate the pressure drop per meter if the solid loading ratio is $2.$

$12.$ Bubble Column Reactors: In a bubble column reactor with a diameter of $0\mathrm{.}5$ m$,$ if the gas flow rate is $0\mathrm{.}01$ m$/$s$,$ estimate the gas holdup assuming homogeneous flow.