(a) Interpretation: An approximate first-order-plus-time-delay transfer function for the given exact transfer function model 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. For higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is: e − θ s = 1 e θ s = 1 1 + θ s ...................(1) Provided the value of θ is very small. The general form of a first-order-plus-time-delay transfer function is: G ( s ) = K e − θ s τ s + 1 ...................(2) Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

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Answer 1

Question

Chapter 6, Problem 6.12E

Interpretation Introduction

(a)

Interpretation:

An approximate first-order-plus-time-delay transfer function for the given exact transfer function model 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.

For higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

Interpretation Introduction

(b)

Interpretation:

The response y(t) for both exact and approximated transfer function are to be simulated plotted for a unit step change in the input on same graph.

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 higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

Interpretation Introduction

(c)

Interpretation:

The maximum error between the two responses for the exact and the approximated model is to be determined along with the time at which this error occurred.

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 higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

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14.9. A forward feed double-effect vertical evaporator, with equal heating areas in each effect, is fed with 5 kg/s of a liquor of specific heat capacity of 4.18 kJ/kg K. and with no boiling point rise, so that 50 per cent of the feed liquor is evaporated. The overall heat transfer coefficient in the second effect is 75 per cent of that in the first effect. Steam is fed at 395 K and the boiling point in the second effect is 373 K. The feed is heated by an external heater to the boiling point in the first effect. It is decided to bleed off 0.25 kg/s of vapour from the vapour line to the second effect for use in another process. If the feed is still heated to the boiling point of the first effect by external means, what will be the change in steam consumption of the evaporator unit? For the purpose of calculation, the latent heat of the vapours and of the steam may both be taken as 2230 kJ/kg

Example(3): It is desired to design a double effect evaporator for concentrating a certain caustic soda solution from 12.5wt% to 40wt%. The feed at 50°C enters the first evaporator at a rate of 2500kg/h. Steam at atmospheric pressure is being used for the said purpose. The second effect is operated under 600mmHg vacuum. If the overall heat transfer coefficients of the two stages are 1952 and 1220kcal/ m2.h.°C. respectively, determine the heat transfer area of each effect. The BPR will be considered and present for the both effect 5:49

العنوان ose only Q Example (7): Determine the heating surface area 개 required for the production of 2.5kg/s of 50wt% NaOH solution from 15 wt% NaOH feed solution which entering at 100 oC to a single effect evaporator. The steam is available as saturated at 451.5K and the boiling point rise (boiling point evaluation) of 50wt% solution is 35K. the overall heat transfer coefficient is 2000 w/m²K. The pressure in the vapor space of the evaporator at atmospheric pressure. The solution has a specific heat of 4.18kJ/ kg.K. The enthalpy of vaporization under these condition is 2257kJ/kg Example (6): 5:48 An evaporator is concentrating F kg/h at 311K of a 20wt% solution of NaOH to 50wt %. The saturated steam used for heating is at 399.3K. The pressure in the vapor space of the evaporator is 13.3 KPa abs. The 5:48 1 J ۲/۱ ostr

Answer 2

Question

Chapter 6, Problem 6.12E

Interpretation Introduction

(a)

Interpretation:

An approximate first-order-plus-time-delay transfer function for the given exact transfer function model 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.

For higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

Interpretation Introduction

(b)

Interpretation:

The response y(t) for both exact and approximated transfer function are to be simulated plotted for a unit step change in the input on same graph.

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 higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

Interpretation Introduction

(c)

Interpretation:

The maximum error between the two responses for the exact and the approximated model is to be determined along with the time at which this error occurred.

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 higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

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Answer 3

Question

Chapter 6, Problem 6.12E

Interpretation Introduction

(a)

Interpretation:

An approximate first-order-plus-time-delay transfer function for the given exact transfer function model 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.

For higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

Interpretation Introduction

(b)

Interpretation:

The response y(t) for both exact and approximated transfer function are to be simulated plotted for a unit step change in the input on same graph.

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 higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

Interpretation Introduction

(c)

Interpretation:

The maximum error between the two responses for the exact and the approximated model is to be determined along with the time at which this error occurred.

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 higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 6, Problem 6.12E

Interpretation Introduction

(a)

Interpretation:

An approximate first-order-plus-time-delay transfer function for the given exact transfer function model 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.

For higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

Interpretation Introduction

(b)

Interpretation:

The response y(t) for both exact and approximated transfer function are to be simulated plotted for a unit step change in the input on same graph.

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 higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

Interpretation Introduction

(c)

Interpretation:

The maximum error between the two responses for the exact and the approximated model is to be determined along with the time at which this error occurred.

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 higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

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See solution

Answer 5

Chapter 6, Problem 6.12E

Interpretation Introduction

(a)

Interpretation:

An approximate first-order-plus-time-delay transfer function for the given exact transfer function model 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.

For higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

Interpretation Introduction

(b)

Interpretation:

The response y(t) for both exact and approximated transfer function are to be simulated plotted for a unit step change in the input on same graph.

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 higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

Interpretation Introduction

(c)

Interpretation:

The maximum error between the two responses for the exact and the approximated model is to be determined along with the time at which this error occurred.

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 higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

Answer 6

Chapter 6, Problem 6.12E

Interpretation Introduction

(a)

Interpretation:

An approximate first-order-plus-time-delay transfer function for the given exact transfer function model 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.

For higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

Answer 7

Chapter 6, Problem 6.12E

Interpretation Introduction

(a)

Interpretation:

An approximate first-order-plus-time-delay transfer function for the given exact transfer function model 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.

For higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

Answer 8

Interpretation Introduction

(b)

Interpretation:

The response y(t) for both exact and approximated transfer function are to be simulated plotted for a unit step change in the input on same graph.

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 higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

Answer 9

Interpretation Introduction

(b)

Interpretation:

The response y(t) for both exact and approximated transfer function are to be simulated plotted for a unit step change in the input on same graph.

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 higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

Answer 10

Interpretation Introduction

(c)

Interpretation:

The maximum error between the two responses for the exact and the approximated model is to be determined along with the time at which this error occurred.

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 higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

Answer 11

Interpretation Introduction

(c)

Interpretation:

The maximum error between the two responses for the exact and the approximated model is to be determined along with the time at which this error occurred.

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 higher-order transfer function approximation, higher-order models are approximated using the time delays into lower-order models of approximate similar dynamics and steady-state characteristics. The formula used for this approximation is:

e−θs=1eθs=11+θs ...................(1)

Provided the value of θ is very small.

The general form of a first-order-plus-time-delay transfer function is:

G(s)=Ke−θsτs+1 ...................(2)

Here, K is the gain of the system, θ is the time delay, and τ is the time constant.

Answer 12

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Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 6 - Prob. 6.1E Ch. 6 - Prob. 6.2E Ch. 6 - Prob. 6.3E Ch. 6 - Prob. 6.4E Ch. 6 - Prob. 6.5E Ch. 6 - Prob. 6.6E Ch. 6 - Prob. 6.7E Ch. 6 - Prob. 6.8E Ch. 6 - Prob. 6.9E Ch. 6 - Prob. 6.10E

Solution Summary: The author explains how an approximate first-order-plus-time-delay transfer function is to be determined.

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Chapter 6 Solutions