Most refrigerators come with a water dispenser that includes an activated carbon "filter". Although called a filter, this is in fact a packed bed with activated carbon particles that have a diameter of

200\mu m

and a void fraction of

\epsi =0.4

. The water inside your house has a pressure of 55 psig, providing enough flow through the carbon packed bed. But over time, the carbon particles get coated with calcium and magnesium oxides, increasing their diameter to

220\mu m

and significantly decreasing the void fraction to

\epsi =0.2

. Calculate the possible flow rate in

(L)/(s)

, assuming exit pressure of zero) through the packed bed before and after clogging occurs. The packed bed has a diameter of 1.5 inches and a length of 12 inches and is horizontal. (15 pts)