Process Engineering and Design Using Visual Basic

474 Pages·2007·18.65 MB·English

by  Arun K. Datta

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Half title page
PROCESS ENGINEERING and
DESIGN USING VISUAL BASIC®
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Title Page
PROCESS ENGINEERING and
DESIGN USING VISUAL BASIC®
ARUN DATTA
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
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Visual Basic and Excel are registered trademarks of Microsoft.
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© 2008 by Taylor & Francis Group, LLC
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Library of Congress Cataloging-in-Publication Data
Datta, Arun.
Process engineering and design using Visual BASIC / Arun Datta.
p. cm.
Includes bibliographical references and index.
ISBN-13: 978-1-4200-4542-0 (alk. paper)
ISBN-10: 1-4200-4542-3 (alk. paper)
1. Chemical processes--Mathematical models. 2. Chemical
processes--Computer simulation. 3. Microsoft Visual BASIC. I. Title.
TP155.7.D36 2006
660’.28--dc22 2006103307
Visit the Taylor & Francis Web site at
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Dedication
To my mother
Smt. Narayani Datta
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Contents
Chapter one Basic mathematics.......................................................................1
Introduction.............................................................................................................1
Physical constants...................................................................................................1
SI prefixes.......................................................................................................1
Mensuration.............................................................................................................2
Triangles..........................................................................................................2
Rectangles.......................................................................................................2
Parallelogram (opposite sides parallel).....................................................3
Rhombus (equilateral parallelogram)........................................................3
Trapezoid (four sides, two parallel)...........................................................3
Quadrilateral (four sided)............................................................................4
Regular polygon of n sides..........................................................................4
Circle................................................................................................................4
Ellipse..............................................................................................................6
Parabola..........................................................................................................6
Prism................................................................................................................6
Pyramid...........................................................................................................7
Right circular cylinder..................................................................................7
Sphere..............................................................................................................7
Right circular cone........................................................................................8
Dished end.....................................................................................................8
Irregular shape...............................................................................................8
Trapezoidal rule.............................................................................................8
Simpson’s rule...............................................................................................8
Irregular volume...........................................................................................9
Algebra.....................................................................................................................9
Factoring.........................................................................................................9
Arithmetic progression.................................................................................9
Geometric progression...............................................................................10
Infinite series (in GP)..................................................................................10
Best fit straight line (least squares method)...........................................10
Binomial equation.......................................................................................11
Polynomial equation...................................................................................11
vii
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viii Process engineering and design using Visual Basic
Maxima/minima.........................................................................................12
Matrix............................................................................................................13
Addition and multiplication of matrices............................................13
Addition of matrices..............................................................................14
Multiplication of matrices.....................................................................14
Matrix properties involving addition.................................................14
Matrix properties involving multiplication.......................................15
Matrix properties involving addition and multiplication...............15
Transpose.................................................................................................15
Symmetric matrix...................................................................................16
Diagonal matrix......................................................................................16
Determinants................................................................................................16
Properties of determinants....................................................................17
Cofactor....................................................................................................18
Determinant and inverses.....................................................................19
Adjoint......................................................................................................19
Cramer’s rule...............................................................................................20
Trigonometry.........................................................................................................21
Functions of circular trigonometry..........................................................21
Periodic functions.......................................................................................22
The magic identity......................................................................................22
The addition formulas................................................................................23
Double angle and half angle.....................................................................23
Product and sum formulas........................................................................24
Relations between angles and sides of triangles...................................25
Law of sines.................................................................................................26
Law of tangents...........................................................................................26
Law of cosines.............................................................................................26
Other relations.............................................................................................26
Inverse trigonometric functions................................................................27
Hyperbolic functions..................................................................................28
Other hyperbolic functions........................................................................29
Inverse hyperbolic functions.....................................................................29
Analytical geometry.............................................................................................30
Straight line..................................................................................................30
Straight line through two points.........................................................30
Three points on one line.......................................................................31
The circle.......................................................................................................31
Tangent.....................................................................................................31
Normal.....................................................................................................32
Four points on a circle...........................................................................32
Circle through three points...................................................................33
Conic section................................................................................................33
Focus.........................................................................................................33
Eccentricity..............................................................................................33
Directrix....................................................................................................33
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Contents ix
Partial derivatives...................................................................................33
Parabola....................................................................................................34
Tangent line with a given slope, m.....................................................36
Ellipse.......................................................................................................36
Hyperbola................................................................................................38
Calculus..................................................................................................................40
Differential calculus....................................................................................40
Understanding the derivatives.................................................................41
Standard derivatives...................................................................................42
Integral calculus..........................................................................................44
Volume of horizontal dished end........................................................44
Volume of vertical dished end.............................................................46
Standard integrals.......................................................................................47
Differential equations...........................................................................................48
First-order differential equations..............................................................48
Separation of variables..........................................................................49
Second-order differential equations.........................................................50
Bessel function........................................................................................51
Partial differential equations...............................................................................52
Laplace transform.......................................................................................60
Standard Laplace transforms....................................................................61
Fourier half-range expansions..................................................................62
Fourier half-range cosine series................................................................63
Fourier half-range sine series....................................................................63
Numerical analysis...............................................................................................65
Solving linear equations (Newton’s method).........................................65
Newton’s method in two variables..........................................................66
Numerical methods in linear algebra......................................................68
Gauss elimination...................................................................................68
Cholesky method....................................................................................70
Numerical integration................................................................................72
Trapezoidal rule......................................................................................72
Simpson’s rule.........................................................................................72
Double integration using Simpson’s rule...............................................75
Numerical solution of first-order differential equations......................76
Euler’s method........................................................................................76
Improved Euler’s method.....................................................................76
Runge–Kutta method.............................................................................77
Second-order differential equations.........................................................79
Runge–Kutta–Nystrom method...........................................................79
Partial differential equations.....................................................................81
Heat conduction problem.....................................................................81
Numerical solution.....................................................................................83
Alternating direction implicit (ADI) method....................................85
Equation of state...................................................................................................90
Boyle’s law and Charles’ law....................................................................90