Chapter 4, Problem 4.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function which relates tank temperature to the inlet liquid temperature is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

The difference in the actual variable $\left(y\right)$ and the original variable $\left(\overline{y}\right)$ is known as deviation variable $\left(y^{\prime }\right)$. It is generally used while modelling a process. Mathematically it is defined as:

$y^{\prime }=y-\overline{y}$

In steady-state process, the accumulation in the process is taken as zero.

Interpretation Introduction

(b)

Interpretation:

The steady-state gain for the transfer function determined in part (a) is to be calculated.

Concept introduction:

In any steady state, the ratio of the amplitude of input signal to the amplitude of the amplifier output is known as steady-state gain. This gain will be same for the entire input range if the amplifier output is linear. For a transfer function, steady-state gain occurs as times tends to infinity which means that in s-domain, this infinite time is represented by $s\to 0$.

Interpretation Introduction

(c)

Interpretation:

It is to be determined if the steady-state gain calculated in part (b) can be unity based on the physical arguments only.

Concept introduction:

In any steady state, the ratio of the amplitude of input signal to the amplitude of the amplifier output is known as steady-state gain. This gain will be same for the entire input range if the amplifier output is linear. For a transfer function, steady-state gain occurs as times tends to infinity which means that in s-domain, this infinite time is represented by $s\to 0$.