Obtain the diameter of the tube from the Re number specification $(10,000)$

and flow rate $-$protein $\frac{?}{hr}*($L$/2$ g$-$protein$)*1000\frac{g}{K}g=500L-$

fluid$/$hr$\}.$ In other words, assume $100\%$ recovery and Fluid flow $=$

Production rate of protein divided by feed concentration of protein.

Assume a critical particle diameter $($transition from diffusion growth to fluid

motion growth$)$ is $1\mathrm{.}0m.$

Use the assumption that:

i$.\frac{\text{p}\text{o}\text{w}\text{e}\text{r}}{\text{v}\text{o}\text{l}\text{u}\text{m}\text{e}}=\frac{(\text{P}\text{r}\text{e}\text{s}\text{s}\text{u}\text{r}\text{e})}{L}$ velocity

ii$.\frac{(\text{P}\text{r}\text{e}\text{s}\text{s}\text{u}\text{r}\text{e})}{L}=\frac{2f(\text{v}\text{e}\text{l}\text{o}\text{c}\text{i}\text{t}\text{y}{)}^2}{\text{d}\text{i}\text{a}\text{m}\text{e}\text{t}\text{e}\text{r}}$

iii. $f=0\mathrm{.}00791$

Calculate the total time in the pipe by addition up the following: Mixing

time, diffusion growth time, and fluid motion time.

Finally, the pipe length is velocity times total time$\mathrm{.}8\mathrm{.}8$ Design of a Tubular Reactor to Precipitate a Protein A protein at a concentration

of $2\mathrm{.}0$ g$/$liter is to be precipitated in a tubular reactor at $20\backslash$deg C and a rate of $1\mathrm{.}0$ kg$/$h$.$ It

is desired that the protein precipitate particles leaving the reactor have a diameter of

$10\backslash$mu m$.$ The properties of the protein are as follows: molecular weight of $480,000,$ diffusion

coeficient of $3\mathrm{.}5\backslash$times $107$ cm$2/$s at $20$C$,$ and precipitate particle density of $1\mathrm{.}29$

g$/$cm$3.$ Design a tubular reactor $($i$.$e$.,$ specify diameter and length$)$ to carry out the precipitation

in turbulent low at a Reynolds number of $10,000.$ It can be assumed that the

particle collision effectiveness factor $(\backslash$alpha $)$ is $0\mathrm{.}05$ for particle growth governed by luid

motion.