Similitude and Approximation Theory

Kline, S.J. J.

ISBN 10: 3642648940 / ISBN 13: 9783642648946

Editore: Springer, 2011

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Dati bibliografici

• Titolo: Similitude and Approximation Theory
• Editore: Springer
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 3642648940
• ISBN 13: 9783642648946
• Rilegatura: Brossura
• Condizione: New

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Riassunto

There are a number of reasons for producing this edition of Simili­ tude and Approximation Theory. The methodologies developed remain important in many areas of technical work. No other equivalent work has appeared in the two decades since the publication of the first edition. The materials still provide an important increase in understanding for first-year graduate students in engineering and for workers in research and development at an equivalent level. In addition, consulting experiences in a number of industries indi­ cate that many technical workers in research and development lack knowledge of the methodologies given in this work. This lack makes the work of planning and controlling computations and experiments less efficient in many cases. It also implies that the coordinated grasp of the phenomena (which is so critical to effective research and develop­ ment work) will be less than it might be. The materials covered in this work focus on the relationship between mathematical models and the physical reality such models are intended v vi Preface to the Springer Edition to portray. Understanding these relationships remains a key factor in simplifying and generalizing correlations, predictions, test programs, and computations. Moreover, as many teachers of engineering know, this kind of understanding is typically harder for students to develop than an understanding of either the mathematics or the physics alone.

Contenuti

Charter 1 Introduction.- 2 Dimensional Analysis and the Pi Theorem Units and Dimensions.- 2-1 Units and Dimensions.- 2-2 Types of Quantities Appearing in Physical Equations.- a. Primary and Secondary Quantities.- b. Physical Constants and Independent Dimensions.- c. Nondimensional Quantities.- 2-3 Dimensional Homogeneity of Physical Equations.- 2-4 Statement and Use of the Pi Theorem.- 2-5 Rationale of the Pi Theorem.- 2-6 Huntley’s Addition.- 2-7 Examples of Application of Dimensional Analysis.- 2-8 Summary.- 3 Method of Similitude and Introduction to Fractional Analysis of Overall Equations.- 3-1 Introduction.- 3-2 Method of Similitude.- a. Use of Force Ratios.- b. Generalization of the Method of Similitude.- c. Some Energy Ratios of Heat Transfer.- 3-3 Direct Use of Governing Overall Equations.- 3-4 Concluding Remarks.- 4 Fractional Analysis of Governing Equations and Conditions.- 4-1 Introduction.- 4-2 Normalization of the Governing Equations.- a. A Procedure for Normalization.- b. Meaning of Normalized Governing Equations.- 4-3 Conditions Required for Rigorous Solution of the Canonical Problem of Similitude and Dimensional Analysis Using Normalized Governing Equations.- 4-4 Basis of Improved Correlations.- a. General Basis.- b. Homogeneous Equations.- 4-5 Relations among Elementary Processes.- a. Model Laws, Similitude, and Analogues.- b. An Alternative Procedure.- c. A Remark on Force Ratios.- d. Relation among Dimensional Analysis, Governing Equations, and Boundary Conditions; Internal and External Similarity.- 4-6 Approximation Theory.- a. Extension to New Classes of Information by Approximation Theory.- b. Classification of Problems and Difficulties in Approximation Theory.- c. Conditions Required for Approximation Theory.- 4-7 Some Problems Involving Uniform Behavior.- 4-8 Nonuniform Behavior―Boundary Layer Methods.- a. Use of Physical Data Alone.- b. Zonal Estimates.- 4-9 Nonuniform Behavior―Expansion Methods and Uniformization.- a. Poincaré’s Expansion.- b. Lighthill’s Expansion.- c. WKBJ Expansion.- d. Inner and Outer Expansions.- 4-10 Processes Involving Transformations of Variables.- a. Absorption of Parameters and Natural Coordinates.- b. Supersonic and Transonic Similarity Rules.- c. Reduction in Number of Independent Variables ― Separation and Similarity Coordinates 179.- 4-11 Summary and Conclusions.- a. Classification of Types of Similitude―Information Achievable from Fractional Analysis of Governing Equations.- b. Various Viewpoints―Relations among Invariance, Transformations, and Similitude.- c. Final Remarks.- 5 Summary and Comparison of Methods.- 5-1 Introduction.- 5-2 Summary of Methods.- a. The Pi Theorem.- b. The Method of Similitude.- c. Use of Governing Equations.- 5-3 Comparison of Methods.- a. Power.- b. Rigor.- c. Accuracy.- d. Simplicity.- e. Input Information.- 5-4 Concluding Remarks.- a. Utility of Various Methods.- b. Implications in Teaching.- c. Possible Further Development.- d. Final Remark.- References.