Problem $1.$ Your job is to design a sieve tray column to distill a mixture of benzene, toluene, and ethylbenzene. The feed is a saturated liquid at a flow rate of $200kg$ moles$/$hr$.$ Under the operating conditions used, the following data is available for the bottom tray in the column.

Temperature $=135\mathrm{.}0C,P=1\mathrm{.}0$ bar

Liquid flow rate $=412\mathrm{.}43$kmo$\frac{l}{h}r$

Vapor flow rate $=324\mathrm{.}21$kmo$\frac{l}{h}r$

Liquid Data:

Mass flow rate $=43,686k\frac{g}{h}r$

Liquid density $=761\mathrm{.}24k\frac{g}{m^3}$

Surface tension $=16\mathrm{.}732dyn\frac{e}{c}m$

Viscosity $=0\mathrm{.}2389cP$

Vapor Data:

Mass flow rate $=34,262k\frac{g}{h}r$

Vapor density $=3\mathrm{.}2255k\frac{g}{m^3}$

Use $=0\mathrm{.}90$ and a tray spacing of $24$ inches. You can assume the column operates at $72\%$ of flooding. Calculate the following based on conditions at the bottom of the column.

a$.C_{sb,f}$

b$.$ Uflood

c$.$ Anet

d$.$ diameter of the column $-$ before and after rounding

Report the diameter in units of feet and round up diameter to nearest half foot. Be careful with units. Remember that $V(\frac{?}{\text{b}\text{a}\text{r}}(MW)V)=W_V$

Problem $2.$ Repeat Problem $1$ except determine the diameter of a packed column that has a vapor flow rate that is at $80\%$ of flooding. Use $2"$ plastic Flexirings for packing. Report the diameter in units of feet and round up diameter to nearest half foot. Show the values of $F,G^{2}F\frac{{}^{0\mathrm{.}2}}{{}_G{}_L{g}_c},,G^{\text{'}}$ flooding, $G^{\text{'}},$ Area, and the diameter of the column before and after rounding. For ${}_{\text{w}\text{a}\text{t}\text{e}\text{r}\text{,}},$ use the density of saturated water at the same temperature $($assume pressure has little effect on density$).$