The volume in the pilot plant feed tank $($B$-01)$ must be kept above $75$ L so that the pump $($P$-01)$ never runs dry.

a$)$ Use a method of your choosing to integrate the flow data through sensor FT$02$ in the second run as a

function of time. If you were unable to extract the run $2$ data in Q$2,$ you may import the FT$02$ data for run

$2$ from $$FT$02\_$run$\_2.$csv$$ in order to complete this question. On Figure $4,$ plot the cumulative volume

versus time on a figure as a blue line, with time units in minutes from the beginning of run $2$ on the x$-$axis.

b$)$ Identify the range of flow data around the value of $75$L that could be accurately described by a linear

relation. Fit a linear regression to this subset of the data and plot the line you obtain on Figure $4$ in red with

line thickness of $3.$ Print to the command window the coefficient of determination $($R

$2$

$)$ for your regression

line and a comment on the goodness of fit of the real data to the regression model.

Note: visual inspection of the flow rate values through FT$02$ should help you identify

the appropriate range of data for the relation.

c$)$ Use the linear relation you obtained in part b$)$ to identify the time in minutes from the beginning of

run $2$ that a total volume of $75$L has flowed into the permeate tank. Plot this as a purple diamond with

marker size $10$ on Figure $4.$