Shape and flow : the fluid dynamics of drag

Citation preview

Ascher H.Shapiro

Shape and Flow The Fluid Dynamics of Drag

M

»i|| / " ■' *■

t • '

I-*.

»

■>-C»

i

* rt' ^

IT' .

Shape and Flow

THE AUTHOR Educated at the Massachusetts Institute of Techno¬ logy (B.S. 1938, Sc.D. 1946), Ascher H. Shapiro has been teaching at M.I.T. since 1938 and now is Pro¬ fessor of Mechanical Engineering. Dr. Shapiro’s speciality was thermodynamics but, with the advent of really high-speed and jet propul¬ sion in World War II, he devoted increasing atten¬ tion to the problems of high-speed gas dynamics. Today he is concerned with all the realms of fluid dynamics, a subject which he believes “wiU never be exhausted, it enters into every aspect of life and technology, and it is forever full of surprise.” For his work as director of a laboratory for the development of torpedo engines in World War II, Dr. Shapiro received the Naval Ordnance Develop¬ ment Award and a certificate of outstanding contri¬ bution from the Departments of War and Navy. A past member of several technical subcommittees of the National Advisory Committee for Aeronautics, Professor Shapiro has been a consultant to the Atomic Energy Commission and on the Technical Advisory Panel on Aeronautics of the Secretary of Defense. As director of Project Dynamo, he evalu¬ ated for the AEC certain economic and technical aspects of nuclear power for civilian use. Dr. Shapiro is a Fellow of the American Academy of Arts and Sciences, and a member of Sigma Xi, Tau Beta Pi, and Pi Tau Sigma. In 1960 he was the recipient of the Richards Memorial Award of the

American Society of Mechanical Engineers “for out¬ standing achievement in engineering.” Author of The Dynamics and Thermodynamics of Compressible Fluid Flow, Professor Shapiro frequently contributes to professional journals. Most recently, he has been interested in teaching engineering with the aid of motion pictures. This has resulted in what Dr. Shapiro hopes will be the first of many films, The Fluid Dynamics of Drag, the source of this book.

4

%'A I

^ rii JiTftVC/' SF^^xjSgJ^^iikUU I ‘i» U." ?» .n >i‘irjAiotrt ''"... 0 ‘i/ •» V'. ■ I r‘arjM(y>ti>jrff J*»-.'.V.v-r > ir .: .-- *H. c«:fUJ4

^ A

* >

,."• f. ■ *v V >'i«' ’..V ..■»■.■ 5 • * } nS' '■••1 •. •

^

At

I * •*•

'

.f>*t '

--.A

‘•M4*'

Shape and Flow THE FLUID DYNAMICS OF DRAG

ASCHER H. SHAPIRO

Published by Anchor Books Doubleday & Company, Inc., Garden City, New York 1961

ACKNOWLEDGMENTS Photographs were reprinted through the courtesy of the following: Figure Figure Figure Figure Figure

1 1 1 1 1

(2): (3): (5): (6): (7):

Figure 13: Figure 28:

WIDE WORLD PHOTO WIDE WORLD PHOTO U. S. AIR FORCE—PhotO

b}’

FICARROTTA

A. DEVANEY, INC. WIDE WORLD PHOTO GEORGE DAFFIN COPE, ESI

Equipment courtesy

Brookfield

ENGINEERING CO.

Figure 37:

NATIONAL AERONAUTICS AND SPACE

Figure 79: Figure 81:

L. PRANDTL, GOTTINGEN

ADMINISTRATION

F.N.M. BROWN, UNIVERSITY OF NOTRE DAME

PHOTOGRAPHS MADE WITH A POLAROID LAND CAMERA BY R. PAUL LARKIN

FROM

MOTION

PICTURES

BY

ABRAHAM

MOROCHNIK

EDUCATIONAL SERVICES INC.

TL 57if

T>1S^ LIBRARY OF CONGRESS CATALOG CARD NUMBER 6I-I258I COPYRIGHT© 1961 BY EDUCATIONAL SERVICES INCORPORATED ALL RIGHTS RESERVED PRINTED IN THE UNITED STATES OF AMERICA FIRST EDITION

ONULP

OF

THE SCIENCE STUDY SERIES The Science Study Series offers to students and to the general public the writing of distinguished authors on the most stirring and fundamental topics of science, from the smallest known particles to the whole uni¬ verse. Some of the books tell of the role of science in the world of man, his technology and civilization. Others are biographical in nature, telling the fasci¬ nating stories of the great discoverers and their dis¬ coveries. All the authors have been selected both for expertness in the fields they discuss and for ability to communicate their special knowledge and their own views in an interesting way. The primary pur¬ pose of these books is to provide a survey within the grasp of the young student or the layman. Many of the books, it is hoped, will encourage the reader to make his own investigations of natural phenomena. The Series, which now offers topics in all the sciences and their applications, had its beginning in a project to revise the secondary schools’ physics curriculum. At the Massachusetts Institute of Tech¬ nology during 1956 a group of physicists, high school teachers, journalists, apparatus designers, film pro¬ ducers, and other specialists organized the Physical Science Study Committee, now operating as part of Educational Services Incorporated, Watertown, Mas¬ sachusetts. They pooled their knowledge and exper¬ ience toward the design and creation of aids to the learning of physics. Initially their effort was sup¬ ported by the National Science Foundation, which

12616

vm

THE SCIENCE STUDY SERIES

has continued to aid the program. The Ford Found¬ ation, the Fund for the Advancement of Education, and the Alfred P. Sloan Foundation have also given support. The Committee has created a textbook, an extensive film series, a laboratory guide, especially designed apparatus, and a teacher’s source book. The Series is guided by a Board of Editors con¬ sisting of Bruce F. Kingsbury, Managing Editor; John H. Durston, General Editor; Paul F. Brandwein, the Conservation Foundation and Harcourt, Brace and Company; Francis L. Friedman, Massachusetts Institute of Technology; Samuel A. Goudsmit, Brookhaven National Laboratory; Philippe LeCorbeiller. Harvard University; and Gerard Piel, Scien¬ tific American.

TO REGINA

i

CONTENTS THE SCIENCE STUDY SERIES

vii

FOREWORD

XV

I INTRODUCTION

19

Our Purpose—The Various Ways That Drag Is Generated II SOME PARADOXICAL EXPERIMENTS

27

The Wind Tunnel—The First Experiment: How Drag of a Sphere Changes with Speed —The Second Experiment: Comparison between the Drags of a Smooth and a Slightly-Roughened Sphere—The Third Experiment: Streamlining in a Slightly Vis¬ cous Fluid—The Fourth Experiment: Streamlining in a Very Viscous Fluid— Summary of the Paradoxes III FUNDAMENTAL CONCEPTS AND PRINCIPLES OF FLUID DYNAMICS The Model of a Continuous Fluid—The Forces Acting on Fluid Particles—Body Forces—Surface Forces—Surface Forces Due to Normal Stresses, or Pressures— Shear Stresses Originating in Viscous Re¬ sistance to Change of Shape—Definition of Viscosity—The No-Slip Condition—The Effect of Pressure on Viscous Friction— Newton’s Law of Motion—Dynamic Sim-

46

XU

SHAPE AND FLOW

ilarity and the Reynolds Number—Deriva¬ tion of the Reynolds Number—An Experi¬ ment on Dynamic Similarity—Further Significance of the Reynolds Number—The Forces on Objects IV VISCOUS-DOMINATED FLOWS AT LOW REYNOLDS NUMBER

84

Some Very Viscous Materials—A More General Concept of Strongly-Viscous Be¬ havior—Stokes’ Law of Drag for Very Low Reynolds Number—The Effect of the Fluid Density V

THE LAW OF DRAG FOR HIGH REYNOLDS NUMBER

99

Experimental Effect of Speed on Drag— The Law of Dynamic Similitude Connect¬ ing Drag Coefficient and Reynolds Number —Dynamic Similitude Is the Foundation of Model Testing VI

THE VISCOUS BOUNDARY LAYER

108

How Important Is Viscosity at High Reyn¬ olds Number?—The Boundary Layer— Effect of Reynolds Number on Growth of Boundary Layer VII VIII

LAMINAR AND TURBULENT FLOWS

122

REDUCTION OF DRAG BY STREAMLINING Experiments in Streamlining—Bernoulli’s Principle for the Flow of a Nonviscous Fluid—The Effect of Viscosity on the Pres-

129

CONTENTS

Xlll

sure Distribution—Boundary-Layer Stall in an Adverse Pressure Gradient—Pressure Drag of Streamlined and Unstreamlined Shapes—Boundary-Layer Visualization— Explanation of the Streamlining Experi¬ ments—Which Is the Better Streamhner: Nature or Man? IX

UNRAVELING OF THE PARADOXES

158

Why Streamlining Increases Drag at Low Reynolds Number—Why an Increase of Speed Sometimes Reduces the Drag—Why Roughness Sometimes Reduces Drag INDEX

173

rf I

-

m

.M

A i*-

'

J

,*•< i»r.i^ •

..•. ^' '.‘ii•

A;r •-‘’■.iv-Sytt)|^ r.r - 4^,-4«

XV

FOREWORD This little book has grown out of a motion picture entitled The Fluid Dynamics of Drag, directed by Quentin Brown and produced by Educational Serv¬ ices Incorporated, Watertown, Massachusetts. The film and the book have the same purpose: to set out clearly some fundamental ideas in fluid dynamics within the context of a number of baffling experi¬ ments on resistance to motion. The book retains the style of experimental action of the film, and bor¬ rows many pictures from the film. While the book is recognizably the film in print, the presentation and the illustrative examples have been adapted to the interests of the reader not hav¬ ing special education in science or engineering. I am indebted to Quentin Brown for many helpful discussions before and during the filming, to the Brookfield Engineering Company for the loan of equipment, to the National Aeronautics and Space Administration for photographs, to the late Ludwig Prandtl for classic film sequences now thirty years old as well as for the inspiration of his style, to Paul Larkin for the skill and artistry with which he has managed the illustrations, and to John H. Durston for constructive suggestions and help in the editorial stages. ASCHER H. SHAPIRO

A rlington, Massachusetts December 1960

■','»

/jrl

\ \v\4jp*. *»^V bAlJtM*/*

li*»Vijir>€id Tit ii,>»ault .'j*^ boi* irvirrfi uilnroP if'T .c4 ,l>5iJirT’*7it 5(iti

|

Jit w'lii A j^r/^f odr vAiC f^i (yi v) iSaom jTMjifj ijriv ,n^ gtu >0 Oi^itliK tuiwatfi^.** tti 3t^J« g — ..ffllii tVt# *^Jlufciiq ykisVt^gox^i i«vxf irfi ^^%a}q4bU(o 2[ytiin;i2wtttv«rii Unu ortJ triPW«:ir>aV^ f3f Jsoi^taliiri tiiii 1 j^b ci titintl.i iMit vonat l>ac snfixl ^•xii^A^ih 3i(j ♦ ^l4#)io