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FUNDAMENTALS OF FLUID DYNAMICS FOR AIRCRAFT DESIGNERS By MAX M. MUNK, PH. D., DR. ENG. CONSULTING ENGINEER Formerly in Charge of Aerodynamic Research, Goettmgen Aerodynamic Institute and National Advisory Committee for Aeronautics THE RONALD PRESS COMPANY NEW YORK This Book Is Dedicated To MR. ADOLPH LEWISOHN PREFACE During the twelve years that the author specialized on aerodynamics, many experiments were made to test various theories, and a considerable number of mathematical formulas were developed by him to explain phenomena as observed in research and flight tests. The results have appeared in more than seventy-five publications listed in the Appendix of this volume. These many separate papers were written without a uniform viewpoint, and the earlier papers lacked the benefit of important data that developed later, consequently it now seems advisable to present the most useful portions of that extensive material for publication as a coordinated volume. At this later date, it has been found practicable to simplify some of the earlier mathematical expressions also, the pro gressive development for formulas, which was necessary to establish their value originally, is no longer essential where such formulas have since been accepted for general use. Fur thermore, at this time it becomes practicable to devote more attention to the applications of the formulas rather than their derivation, together with comments on their relation to other theories in fact that is the primary purpose of this book. The short, simple formulas that are coming into use by aircraft designers can be employed to far better advantage by an understanding of the fundamental principles from which they have evolved. The manner of presenting herein the fundamentals of fluid dynamics as a digest of the theories that have withstood the test of time and trial, has in view the usefulness particularly for teachers, students of aeronautical engineering, and the designers of airplanes and airships. Our knowledge of air motions is still very imperfect and chiefly the product of direct experience even the results of vi PREFACE research experiments are often difficult to grasp. Nor is our theoretical knowledge really very wide However, there are a few simple relations that are exceedingly practical, and actually having so few, we should be eager to retain and use them. Because we are largely dependent on tests, there is even a greater need at this time for systematizing the immense amount of empirical information into a form suitable for persons en gaged in this rapidly developing science. It is the authors earnest hope that this work will prove useful in disseminating a clearer conception of available knowledge relating to air motion in its application to flight phenomena. It is pleasant duty to express thanks to Mr. Frederick N. Esher for most valuable assistance in pointing out errors in the manuscript, checking the mathematics, and providing the solutions to the problems in the text, as well as general sug gestions leading to improvements in the book. Washington, D. C, MAX M. MUNK. February 4, 1929. CONTENTS SYMBOLS USED IN Tms BOOK INTRODUCTION PAGE xi CHAPTER I THE CLASSICAL PRINCIPLES OP HYDRODYNAMICS . ... 6 Rotation - Velocity potential - Air pressure - Condition of mcomprea sibility - Kinetic energy, momentum and apparent mass. CHAPTER n THE AERODYNAMIC FORCES ON AIRSHIP HULLS ........ 20 Resultant airship force in straight motion - In circular path - Distribu tion along the axis - Pressure distribution over the bow of the hull - Distribution around the cross-section of the hull - Size of fins - Flying in a circle - Flying through gusts. CHAPTER HE THE POTENTIAL FLOW or THE STRAIGHT LINE ......... 47 Potential functions - Flows around a straight line - Synopsis. CHAPTER IV THEORY or THE WING SECTION ...............





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