Please help out with both and show working as much as possible. Thank you!

Problem $3(20$ pts$)$

A bioreactor for culturing NS$0$ cells has a working volume of $35m^3.$ Dry air $,$

$79\%N_2$ and free of moisture$)$ at $37C$ and $1$atm is supplied at $25\frac{m^3}{m}in.$ The dissolved

oxygen in the bioreactor is $25\%$ of saturation with ambient air. The outlet gas composi$-$

tion is $15\%O_2,4\mathrm{.}5\%C{O}_2,6\%H_{2}O$ and the balance $N_2.$

$($a$)$ Calculate the oxygen uptake rate $($OUR$)$ in mmol$\frac{O_2}{L}-h$ assuming that the OUR

is equal the oxygen transfer rate $($OTR$).$

$($b$)$ Calculate the $K_L$a for the transfer of oxygen in this system.

The cells are cultured at $37C.$ Ideal gas constant: $R=0\mathrm{.}082$atm$**L^{**}mo{l}^{-1}**K^{-1}.$

Problem $4(20$ pts$)$

CHO cells are cultured in a $10,000-$liter stirred$-$suspension bioreactor to produce a mono$-$

clonal antibody. The bioreactor diameter is $3m$ and the impeller diameter is half of that.

The culture is stirred at $120rpm.$ For the type of impeller that the bioreactor system is

equipped with, the power number has a value of $1\mathrm{.}2$ when the impeller Reynolds number

is greater than $5{10}^4.$ If the density and viscosity of the culture media are $993k\frac{g}{m^3}$ and

$6\mathrm{.}913{10}^{-4}P{a}^{**}s,$ respectively, calculate the:

$($a$)$ Impeller Reynolds number for the culture conditions and bioreactor characteris$-$

tics described above,

$($b$)$ Required power of the motor,

$($c$)$ Power per unit volume,

$($d$)$ Tip speed of the impeller.