A diffused aeration unit is being tested in a batch

liquid reactor consisting of a $3-$m deep tank filled

with $100$m$3$ of water at $20$C$.$ The gas being injected

is pure O$2,$ and the diameter of the injected bubbles at

the diffuser surface is $3\mathrm{.}0$ mm$.$ For the experimental conditions,Hpc forO$2$ is $0$:$019$ atmL$=$mg$.$ The gas flow

rate is $120$SCM$/$h$.$ Assume that the pressure throughout

the tank can be approximated as the pressure at

mid$-$depth, and that the pressure at the water surface

is $1\mathrm{.}0$ atm.

$($a$)$ Assuming that the bubbles rise at an average

velocity determined by their diameter at middepth,

and that a negligible fraction of the

total O$2$ transfers out of the bubbles, estimate

the total interfacial area in the tank at any

instant.

$($b$)$ If the water in the tank is initially in equilibrium

with air, and the concentration of dissolved O$2$

increases to $31\mathrm{.}0$ mg$/$L after $10$ min of aeration,

what is KL$?$