Problem $3.(30$ pts$)$ A single$-$tank process has been operating for a long period of time with the inlet flow

rate equal to $30\mathrm{.}1f\frac{t^3}{m}in.$ After the operator suddenly increases the flow rate at $t=0$ by $10\%,$ the liquid

level $h$ in the tank changes, as shown in Table $1.$

Table $1$

Assuming that a first$-$order model can describe the process dynamics,

a$.(10$ pts$)$ Calculate the steady$-$state gain and the time constant using the

time required for the output to reach $63\mathrm{.}2\%$ of the total change.

b$.(10$ pts$)$ Calculate the time constant using the initial slope of the response

curve.

c$.(10$ pts$)$ Compare the data and the two models $($sections a and b$)$ by

simulating their step responses.