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Theory of jets in ideal fluids
Book Reviews it would seem appropriate at this juncture to have discussed, e.g., the adjoint flux and its ramifications, both physical and mathematical. Instead, the adjoint is relegated to the appendix where the usual austere definition of the adjoint operator in terms of scalar products of functions is given. Monoenergetic neutron transport, including the few classical examples solvable in closed form is discussed in Chapter 3. This includes the well-known Milne problem for a half space. Some properties of the solutions of the transport equations are obtained using the variational method; the latter being developed in the appendix. Expansions of the solutions of the monoenergetic transport equation in terms of orthogonal polynomials is discussed in Chapter 4; again the classical tutorial examples are used. The fifth chapter derives the diffusion equation approximation to the transport equation, outlining the conditions under which it is valid. The next two chapters discuss the important, but mathematically formidable, situation in which energy dependence, with and without special dependence, plays a role in the transport equation solution schema. Most of the better known pertinent approximations are displayed with pedantic neatness. The eighth and last chapter considers digital computer numerical approximations to the energy and space dependent transport problem. The Monte Carlo method is dispatched in one section. S~, multi-group and perturbation methods follow in scholarly precision. Three appendices, a bibliography and the usual diaphanous index are also included. As presented, this book would provide a good basis for a one-semester graduate course, or seminar, in transport theory. It is realized that conflicts arise when writing a monograph-type book and that the author is torn between the amount of material to include or omit. However, this book does a good job of deftly stringing the pearls of neutron transport theory together into an attractive and serviceable package. MILTON ASH
E. H. Plesset Associa~, Inc. Santa Manic,a, California
362
THEORY OF JETS IN IDEAL FLUIDS, by N. I. Gurevich. Russian trans, by R. L. Street and K. Zagustin. 585 pages, diagrams, 6 X 9 in. New York, Academic Press, Inc., 1965. Price, $15.00. A systematic description of the most important analytical treatments of jets in ideal fluids is the substance of this presentation. The theory of plane jet flows is introduced in Chapter 1. The author reviews the method of complex variables and its application to the study of two-dimensional, plane, potential flows of incompressible fluids. This review is followed by a discussion of the basic assumptions underlying the jet theory, and of the methods of Kirchhoff (extension of Helmholtz's solutions), Zhukovskii, and Chaplygin. In Chapter 2 the author discusses the flow from a vessel with oblique walls, flow through a symmetric orifice in a rectangular vessel, flow from an opening between two fiat plates, flow through a Borda nozzle, flow from a channel through suction slots, and from rectangular vessels through orifices located at one or two comers. Chapter 3 deals with flows past polygonal obstacles. The flows around curvilinear obstacles are discussed in Chapter 4. Levi-Civita's method is dealt with, and the equations for the resultant force and moment acting on an obstacle are derived. This is followed by a discussion of flow around a circular cylinder, and by the general method (of Sedov) for the solution of flows around several curvilinear arcs. Chapter 5 entitled "Flow Around a Body at Small Cavitation Number" gives a brief discussion of the phenomenon of cavitation, discusses the cavitating flow around a flat plate (using the Efros re-entrant jet model), the symmetric cavitating flow around a wedge, and the cavitating flow around a thin profile. Chapter 6 deals with the flow of limited jets around obstacles. The discussion includes a flow around a symmetric and asymmetric wedge, around a flat plate in a free jet and in a channel, of a flow around a fiat plate in the presence of a wall, of a cascade flow without and with cavitation, and of a flow around a cylinder between two walls. The chapter on the planing surfaces and
Journal of The Frs~klln Institute
Book Reviews hydrofoils begins with a description of the phenomenon of planing (or gliding) of a flat plate. This is followed by a discussion of planing of tandem flat plates, and of hydrofoils beneath a free surface. Chapter 8 deals with various free-Jet phenomena, such as collision of jets, with a brief discussion of the hollow charges and armor-piercing jets, and of jets with singularities. Chapter 9 deals with unsteady jet flows, such as the flow produced by an accelerating flat plate or a streamlined contour, of weakly perturbed jet flows, and of the surface impact of a wedge. Next, the jets in compressible fluids are covered. The author presents Chaplygin's equations and their exact solutions for a subsonic flow, and also Chaplygin's approximate method for small Mach numbers and its extensions. Then axisymmetric jet flows follow. Here the approximate methods of solution are dealt with, and a survey of references on axisymmetric jet flows given. The chapter ends with a discussion of the asymptotic law of jet shape. In the final
presentation the author discusses briefly the jet flow in the presence of gravity forces (considering only those flows in which surface waves are absent), and the effects of the surface tension. The book represents a very valuable addition to the literature on jets in ideal fluids. The concise discussions of various jet problems are very well presented and the equations systematically derived. Almost all solutions are presented in detail. Many comparisons of the calculated results with experimental data are given. It supplements well the earlier book: "Jets, Wakes, and Cavities" by G. Birkhoff and E. H. Zarantonello (Academic Press, 1957) which is less detailed but includes a discussion of steady viscous wakes and jets, periodic wakes and turbulent wakes and jets, and a chapter on the existence and uniqueness theorems. The book has a list of 262 references, 110 of them being Russian. JERZY A. OWCZAREK
Department of Mechanical Engineering Lehigh University Bethlehem, Pennsylvania
Book Notes ASTRONAUTICS FOR SCIENCE TEACHERS, by John G. Meitner. 381 pages, diagrams, illustrations, 6 X 9 in. New York, John Wiley & Sons, 1965. Price, $8.95.
This represents one of the few texts on astronautics which is specifically prepared for science teachers. It is written by experts in various fields of astronautics who are experienced writers, researchers and lecturers. Three chapters of a general nature sweep across the entire field of astronautics. Six chapters, of specialized content, are organized around the individual scientific disciplines-physics, biology, mathematics, etc. A highly intriguing concluding chapter deals extensively with methods and aids for introducing the material in the classroom. A bibliography, references, text books, encyclopedias and atlases, periodicals, audio visual materials, and sources of free and inexpensive materials complete the book. This feature is a much needed and valuable one for the science teacher who would like to build a course around this subject.
Vol. 281,No. 4, April 1966
THE COSMOS ACCORDINGTO CAUSATION,by Haviland Hull Platt. 63 pages, 5 X 8 in. New York, Exposition Press, 1965. $5.00. As the author states in his introduction: "After the introduction by Einstein of the Theory of Relativity there were hopes that at last the road was open toward a basic system capable of providing a general unification of physical phenomena. These hopes have not been realized. On the contrary, a survey of theory today discloses a far greater array of contradictions, empiricisms and theoretical dead ends than were in evidence in pre-Einstein times. "This situation has raised serious doubts in many quarters about the validity of theories that have through the ages stood as the foundation stones of our environmental world. Foremost among these is causation." "The reader of this book is in for some very interesting . . . surprises. He is going to experience a novel approach to a scientifically popular topic." (From the Foreword by Wynn Laurence LePage, President. Franklin Inst.)
363
E. H. Plesset Associa~, Inc. Santa Manic,a, California
362
THEORY OF JETS IN IDEAL FLUIDS, by N. I. Gurevich. Russian trans, by R. L. Street and K. Zagustin. 585 pages, diagrams, 6 X 9 in. New York, Academic Press, Inc., 1965. Price, $15.00. A systematic description of the most important analytical treatments of jets in ideal fluids is the substance of this presentation. The theory of plane jet flows is introduced in Chapter 1. The author reviews the method of complex variables and its application to the study of two-dimensional, plane, potential flows of incompressible fluids. This review is followed by a discussion of the basic assumptions underlying the jet theory, and of the methods of Kirchhoff (extension of Helmholtz's solutions), Zhukovskii, and Chaplygin. In Chapter 2 the author discusses the flow from a vessel with oblique walls, flow through a symmetric orifice in a rectangular vessel, flow from an opening between two fiat plates, flow through a Borda nozzle, flow from a channel through suction slots, and from rectangular vessels through orifices located at one or two comers. Chapter 3 deals with flows past polygonal obstacles. The flows around curvilinear obstacles are discussed in Chapter 4. Levi-Civita's method is dealt with, and the equations for the resultant force and moment acting on an obstacle are derived. This is followed by a discussion of flow around a circular cylinder, and by the general method (of Sedov) for the solution of flows around several curvilinear arcs. Chapter 5 entitled "Flow Around a Body at Small Cavitation Number" gives a brief discussion of the phenomenon of cavitation, discusses the cavitating flow around a flat plate (using the Efros re-entrant jet model), the symmetric cavitating flow around a wedge, and the cavitating flow around a thin profile. Chapter 6 deals with the flow of limited jets around obstacles. The discussion includes a flow around a symmetric and asymmetric wedge, around a flat plate in a free jet and in a channel, of a flow around a fiat plate in the presence of a wall, of a cascade flow without and with cavitation, and of a flow around a cylinder between two walls. The chapter on the planing surfaces and
Journal of The Frs~klln Institute
Book Reviews hydrofoils begins with a description of the phenomenon of planing (or gliding) of a flat plate. This is followed by a discussion of planing of tandem flat plates, and of hydrofoils beneath a free surface. Chapter 8 deals with various free-Jet phenomena, such as collision of jets, with a brief discussion of the hollow charges and armor-piercing jets, and of jets with singularities. Chapter 9 deals with unsteady jet flows, such as the flow produced by an accelerating flat plate or a streamlined contour, of weakly perturbed jet flows, and of the surface impact of a wedge. Next, the jets in compressible fluids are covered. The author presents Chaplygin's equations and their exact solutions for a subsonic flow, and also Chaplygin's approximate method for small Mach numbers and its extensions. Then axisymmetric jet flows follow. Here the approximate methods of solution are dealt with, and a survey of references on axisymmetric jet flows given. The chapter ends with a discussion of the asymptotic law of jet shape. In the final
presentation the author discusses briefly the jet flow in the presence of gravity forces (considering only those flows in which surface waves are absent), and the effects of the surface tension. The book represents a very valuable addition to the literature on jets in ideal fluids. The concise discussions of various jet problems are very well presented and the equations systematically derived. Almost all solutions are presented in detail. Many comparisons of the calculated results with experimental data are given. It supplements well the earlier book: "Jets, Wakes, and Cavities" by G. Birkhoff and E. H. Zarantonello (Academic Press, 1957) which is less detailed but includes a discussion of steady viscous wakes and jets, periodic wakes and turbulent wakes and jets, and a chapter on the existence and uniqueness theorems. The book has a list of 262 references, 110 of them being Russian. JERZY A. OWCZAREK
Department of Mechanical Engineering Lehigh University Bethlehem, Pennsylvania
Book Notes ASTRONAUTICS FOR SCIENCE TEACHERS, by John G. Meitner. 381 pages, diagrams, illustrations, 6 X 9 in. New York, John Wiley & Sons, 1965. Price, $8.95.
This represents one of the few texts on astronautics which is specifically prepared for science teachers. It is written by experts in various fields of astronautics who are experienced writers, researchers and lecturers. Three chapters of a general nature sweep across the entire field of astronautics. Six chapters, of specialized content, are organized around the individual scientific disciplines-physics, biology, mathematics, etc. A highly intriguing concluding chapter deals extensively with methods and aids for introducing the material in the classroom. A bibliography, references, text books, encyclopedias and atlases, periodicals, audio visual materials, and sources of free and inexpensive materials complete the book. This feature is a much needed and valuable one for the science teacher who would like to build a course around this subject.
Vol. 281,No. 4, April 1966
THE COSMOS ACCORDINGTO CAUSATION,by Haviland Hull Platt. 63 pages, 5 X 8 in. New York, Exposition Press, 1965. $5.00. As the author states in his introduction: "After the introduction by Einstein of the Theory of Relativity there were hopes that at last the road was open toward a basic system capable of providing a general unification of physical phenomena. These hopes have not been realized. On the contrary, a survey of theory today discloses a far greater array of contradictions, empiricisms and theoretical dead ends than were in evidence in pre-Einstein times. "This situation has raised serious doubts in many quarters about the validity of theories that have through the ages stood as the foundation stones of our environmental world. Foremost among these is causation." "The reader of this book is in for some very interesting . . . surprises. He is going to experience a novel approach to a scientifically popular topic." (From the Foreword by Wynn Laurence LePage, President. Franklin Inst.)
363