A packed bed that consists of the same medium as that in Problem 3 is to be used to filter solids from an aqueous slurry. To determine the filter properties, you test a small section of the bed, which is 6 in. in diameter and 6 in. deep, in the lab. When the slurry is pumped through this test model at a constant flow rate of $30 \mathrm{gpm}$, the pressure drop across the bed rises to $2 \mathrm{psia}$ after $10 \mathrm{~min}$. How long will it take to filter $100,000 \mathrm{gal}$ of water from the slurry in a full-size bed, which is $10 \mathrm{ft}$ in diameter and $2 \mathrm{ft}$ deep, if the slurry is maintained at a depth of $2 \mathrm{ft}$ over the bed and drains by gravity through the bed?

Problem 3

A trickle bed filter is composed of a packed bed of broken rock that has a shape such that the average ratio of the surface area to volume for the rock particles is $30 \mathrm{in} .^{-1}$ The bed is $2 \mathrm{ft}$ deep, has a porosity of 0.3 , and is covered by a layer of water that is $2 \mathrm{ft}$. deep and drains by gravity through the bed.

(a) Determine the volume flow rate of the water through the bed per unit bed area (in $\mathrm{gpm} / \mathrm{ft}^{2}$ ).

(b) If the water is pumped upward through the bed (e.g., to flush it out), calculate the flow rate (in $\mathrm{gpm} / \mathrm{ft}^{2}$ of bed area) that would be required to fluidize the bed.

(c) Calculate the corresponding flow rate that would sweep the rock particles away with the water. The rock density is $120 \mathrm{lb}_{\mathrm{m}} / \mathrm{ft}^{3}$.