The accompanying figure depicts a distillation column that is used in a petroleum plant to fractionate $($i$.$e$.$ separate$)$ a liquid feed stream containing equimolar amounts of benzene and toluene. The 'overhead product' $($from the reflux drum$)$ contains mostly the lighter benzene component while the 'bottoms product' $($from the reboiler$)$ contains mostly the heavier toluene component.

In the bottom half of the column $($known as the 'stripping section'$),$ there is always some 'bottoms liquid' $($approximately $10\%$ benzene and $90\%$ toluene with corresponding density of $791k\frac{g}{m^3})$ that sits in the base of the column. A $23-10$ centrifugal pump with an $8"$ impeller $($see pump performance curve below$)$ is used to transfer $275ga\frac{l}{m}in$ of this hot 'bottoms liquid' to a reboiler where a portion of it gets vaporized and sent back to the column and the rest gets removed as the 'bottoms product'.

a$.$ Determine the value of $NPS{H}_R(m)$ for the 'bottoms liquid' pump to operate at the desired flow rate of $275ga\frac{l}{m}in.$

b$.$ If the average height of the 'bottoms liquid' at the base of the column is $2m,$ determine what is the appropriate vertical position $)$ of the $23-10$ centrifugal pump relative to the bottom of the column for the following conditions:

The pressure inside the column is fairly constant at $1\mathrm{.}5$atm throughout the column

The temperature varies inside the column; the temperature at the bottom is approximately $100C$ and the corresponding vapour pressure of the 'bottoms liquid' is $75$kPa

It has been determined that the total head loss $($i$.$e$.$ all friction and minor losses$)$ for the suction piping into the pump can be appropriately described by the equation $H_{l_T}=6\mathrm{.}83*Q^2,$ where $H_{l_T}$ is in $m$ and $Q$ is in $\frac{m^3}{m}in.$

$3$The accompanying figure depicts a distillation column that is used in a

petroleum plant to fractionate $($i$.$e$.$ separate$)$ a liquid feed stream

containing equimolar amounts of benzene and toluene. The $$overhead

product$($from the reflux drum$)$ contains mostly the lighter benzene

component while the $$bottoms product$($from the reboiler$)$ contains

mostly the heavier toluene component.

In the bottom half of the column $($known as the $$stripping section$),$ there

is always some $$bottoms liquid$($approximately $10\%$ benzene and $90\%$

toluene with corresponding density of $791$ kg$/$m$3$

$)$ that sits in the base of

the column.