Fluid Mechanics - E.Krause.pdf - Pneumatyka i Hydraulika - Automation_Engineering

Egon Krause

Fluid Mechanics

Egon Krause

Fluid Mechanics

With Problems and Solutions,

and an Aerodynamic Laboratory

With 607 Figures

Prof. Dr. Egon Krause

RWTH Aachen

Aerodynamisches Institut

Wullnerstr.5-7

52062 Aachen

Germany

ISBN 3-540-22981-7 Springer Berlin Heidelberg New York

Library of Congress Control Number: 2004117071

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is concerned, speciﬁcally the rights of translation, reprinting, reuse of illustrations, recitation, broa-

dcasting, reproduction on microﬁlm or in other ways, and storage in data banks. Duplication of this

publication or parts thereof is permitted only under the provisions of the German Copyright Law

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Preface

During the past 40 years numerical and experimental methods of ﬂuid mechanics were sub-

stantially improved. Nowadays time-dependent three-dimensional ﬂows can be simulated on

high-performance computers, and velocity and pressure distributions and aerodynamic forces

and moments can be measured in modern wind tunnels for ﬂight regimes, until recently not

accessible for research investigations. Despite of this impressive development during the recent

past and even 100 years after Prandtl introduced the boundary-layer theory, the fundamentals

are still the starting point for the solution of ﬂow problems. In the present book the important

branches of ﬂuid mechanics of incompressible and compressible media and the basic laws de-

scribing their characteristic ﬂow behavior will be introduced. Applications of these laws will be

discussed in a way suitable for engineering requirements.

The book is divided into the six chapters: Fluid mechanics I and II, exercises in ﬂuid mechan-

ics, gas dynamics, exercises in gasdynamics, and aerodynamics laboratory. This arrangement

follows the structure of the teaching material in the ﬁeld, generally accepted and approved for

a long time at German and foreign universities. In ﬂuid mechanics I, after some introductory

statements, incompressible ﬂuid ﬂow is described essentially with the aid of the momentum

and the moment of momentum theorem. In ﬂuid mechanics II the equations of motion of ﬂuid

mechanics, the Navier-Stokes equations, with some of their important asymptotic solutions are

introduced. It is demonstrated, how ﬂows can be classiﬁed with the aid of similarity param-

eters, and how speciﬁc problems can be identiﬁed, formulated and solved. In the chapter on

gasdynamics the inﬂuence of variable density on the behavior of subsonic and supersonic ﬂows

is described.

In the exercises on ﬂuid mechanics I and II and on gasdynamics the material described in the

previous chapters is elaborated in over 200 problems, with the solutions presented separately.

It is demonstrated how the fundamental equations of ﬂuid mechanics and gasdynamics can be

simpliﬁed for the various problem formulations and how solutions can be constructed. Numer-

ical methods are not employed. It is intended here, to describe the fundamental relationships

in closed form as far as possible, in order to elucidate the intimate connection between the

engineering formulation of ﬂuid-mechanical problems and their solution with the methods of

applied mathematics. In the selection of the problems it was also intended, to exhibit the many

diﬀerent forms of ﬂows, observed in nature and technical applications.

Because of the special importance of experiments in ﬂuid mechanics, in the last chapter, aero-

dynami cs laboratory, experimental techniques are introduced. It is not intended to give a com-

prehensive and complete description of experimental methods, but rather to explain with the

description of experiments, how in wind tunnels and other test facilities experimental data can

be obtained.

A course under the same title has been taught for a long time at the Aerodymisches Institut

of the RWTH Aachen. In the various lectures and exercises the functioning of low-speed and

supersonic wind tunnels and the measuring techniques are explained in experiments, carried

out in the facilities of the laboratory. The experiments comprise measurements of pressure

distributions on a half body and a wing section, of the drag of a sphere in incompressible and

compressible ﬂow, of the aerodynmic forces and their moments acting on a wing section, of

velocity proﬁles in a ﬂat-plate boundary layer, and of losses in compressible pipe ﬂow. Another

important aspect of the laboratory course is to explain ﬂow analogies, as for example the

VI Preface

so-called water analogy, according to which a pressure disturbance in a pipe, ﬁlled with a

compressible gas, propagates analogously to the pressure disturbance in supercritical shallow

water ﬂow.

This book was stimulated by the friendly encouragement of Dr. M. Feuchte of B.G. Teubner-

Verlag. My thanks go also to Dr. D. Merkle of the Springer-Verlag, who agreed to publish

the English translation of the German text. Grateful acknowledgement is due to my successor

Professor Dr.-Ing. W. Schroder, who provided personal and material support by the Aerody-

namisches Institut in the preparation of the manuscript. I am indebted to Dr.-Ing. O. Thomer

who was responsible for the preparatory work during the initial phase of the project until he

left the institute. The ﬁnal manuscript was prepared by cand.-Ing. O. Yilmaz, whom I grate-

fully acknowledge. Dr.-Ing. M. Meinke oﬀered valuable advice in the preparation of some of the

diagrams.

Aachen, July 2004

E. Krause

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