(a) Interpretation: The transfer function H ′ ( s ) Q ′ i ( s ) for both the tanks is to be determined. Concept introduction: For chemical processes, dynamic models consisting of 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 ( y ) and the original variable ( y ¯ ) is known as the deviation variable ( y ′ ) .It is generally used while modeling a process. Mathematically it is defined as: y ′ = y − y ¯ In the steady-state process, the accumulation in the process is taken as zero.

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Answer 1

Question

Chapter 5, Problem 5.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function H′(s)Q′i(s) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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 (y) and the original variable (y¯) is known as the deviation variable (y′) .It is generally used while modeling a process. Mathematically it is defined as:

y′=y−y¯

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

Interpretation Introduction

(b)

Interpretation:

The transient response of h(t) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

Interpretation Introduction

(c)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)]

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Interpretation Introduction

(d)

Interpretation:

The tank that will overflow first and the time of overflow is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

Interpretation Introduction

(e)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

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Students have asked these similar questions

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Answer 2

Question

Chapter 5, Problem 5.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function H′(s)Q′i(s) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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 (y) and the original variable (y¯) is known as the deviation variable (y′) .It is generally used while modeling a process. Mathematically it is defined as:

y′=y−y¯

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

Interpretation Introduction

(b)

Interpretation:

The transient response of h(t) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

Interpretation Introduction

(c)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)]

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Interpretation Introduction

(d)

Interpretation:

The tank that will overflow first and the time of overflow is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

Interpretation Introduction

(e)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

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Answer 3

Question

Chapter 5, Problem 5.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function H′(s)Q′i(s) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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 (y) and the original variable (y¯) is known as the deviation variable (y′) .It is generally used while modeling a process. Mathematically it is defined as:

y′=y−y¯

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

Interpretation Introduction

(b)

Interpretation:

The transient response of h(t) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

Interpretation Introduction

(c)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)]

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Interpretation Introduction

(d)

Interpretation:

The tank that will overflow first and the time of overflow is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

Interpretation Introduction

(e)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

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Answer 4

Question

Chapter 5, Problem 5.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function H′(s)Q′i(s) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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 (y) and the original variable (y¯) is known as the deviation variable (y′) .It is generally used while modeling a process. Mathematically it is defined as:

y′=y−y¯

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

Interpretation Introduction

(b)

Interpretation:

The transient response of h(t) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

Interpretation Introduction

(c)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)]

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Interpretation Introduction

(d)

Interpretation:

The tank that will overflow first and the time of overflow is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

Interpretation Introduction

(e)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

Expert Solution & Answer

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Answer 5

Chapter 5, Problem 5.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function H′(s)Q′i(s) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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 (y) and the original variable (y¯) is known as the deviation variable (y′) .It is generally used while modeling a process. Mathematically it is defined as:

y′=y−y¯

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

Interpretation Introduction

(b)

Interpretation:

The transient response of h(t) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

Interpretation Introduction

(c)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)]

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Interpretation Introduction

(d)

Interpretation:

The tank that will overflow first and the time of overflow is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

Interpretation Introduction

(e)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

Answer 6

Chapter 5, Problem 5.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function H′(s)Q′i(s) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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 (y) and the original variable (y¯) is known as the deviation variable (y′) .It is generally used while modeling a process. Mathematically it is defined as:

y′=y−y¯

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

Answer 7

Chapter 5, Problem 5.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function H′(s)Q′i(s) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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 (y) and the original variable (y¯) is known as the deviation variable (y′) .It is generally used while modeling a process. Mathematically it is defined as:

y′=y−y¯

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

Answer 8

Interpretation Introduction

(b)

Interpretation:

The transient response of h(t) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

Answer 9

Interpretation Introduction

(b)

Interpretation:

The transient response of h(t) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

Answer 10

Interpretation Introduction

(c)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)]

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Answer 11

Interpretation Introduction

(c)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)]

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Answer 12

Interpretation Introduction

(d)

Interpretation:

The tank that will overflow first and the time of overflow is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

Answer 13

Interpretation Introduction

(d)

Interpretation:

The tank that will overflow first and the time of overflow is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

Answer 14

Interpretation Introduction

(e)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

Answer 15

Interpretation Introduction

(e)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of 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.

Answer 16

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Answer 17

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Answer 18

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Answer 19

Ch. 5 - Prob. 5.1E Ch. 5 - Prob. 5.2E Ch. 5 - Prob. 5.3E Ch. 5 - Prob. 5.4E Ch. 5 - Prob. 5.5E Ch. 5 - Prob. 5.6E Ch. 5 - Appelpolscher has just left a meeting with Stella...Ch. 5 - Prob. 5.8E Ch. 5 - Prob. 5.9E Ch. 5 - Prob. 5.10E

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Chapter 5 Solutions