Prandtl was one of the great theorists of aerodynamics and this work has long been considered one of the finest introductory works in the field. Topics include flow through pipes, Prandtl's own work on boundary layers, drag, airfoil theory, and entry conditions for flow in a pipe.
ENGINEERING SOCIETIES MONOGRAPHS
PREFACE
INTRODUCTION
CHAPTER 1 ELEMENTS OF HYDRODYNAMICS
1. The Equation of Euler for One-dimensional Flow
2. The Equation of Bernoulli for One-dimensional Flow; Three-dimensional Equation of Euler
3. Definition of Viscosity; Equation of Navier-Stokes
CHAPTER II LAWS OF SIMILARITY
4. The Law of Similarity under the Action of Inertia and Viscosity
5. The Law of Similarity under the Action of Inertia and Gravity
6. Relation between Considerations of Similarity and Dimensional Analysis
CHAPTER III FLOW IN PIPES AND CHANNELS
A. Laminar Flow
8. General
9. The Fundamental Investigation of Hagen
10. The Investigation of Poiseuille
11. The Law of Hagen-Poiseuille
12. Derivation of Hagen-Poiseuille's Law from Newton's Viscosity Law
13. Limits of the Validity of the Hagen-Poiseuille Law
14. Phenomena Near the Entrance of the Tube
15. The Length of Transition
16. The Pressure Distribution in the Region Near the Entrance
17. The Correction Term for Kinetic Energy
18. The Velocity Distribution in the Region Near the Entrance
19. The Pressure Drop in the Entrance Region in the Case of Laminar Flow
20. The Importance of the Pressure Drop in the Entrance Region for Viscosity Measurements
B. The Transition between Laminar and Turbulent Flow
21. The First Investigations by Hagen
22. The Fundamental Investigation by Reynolds
23. The Critical Reynolds' Number
24. Influence of the Initial Disturbance on the Critical Reynolds' Number
25. The Conditions at the Transition between Laminar and Turbulent Flow
26. Intermittent Occurrence of Turbulence
27. Measurements of Pressure Drop at the Transition between Laminar and Turbulent Flow
28. Independence of the Critical Reynolds' Number of the Length of the Tube
C. Turbulent Flow
29. Historical Formulas for the Pressure Drop
30. The Resistance Formula of Blasius for Smooth Tubes
31. The Resistance Law for Rough Tubes
32. Roughness and Waviness of the Walls
33. Measurement of the Mean Velocity of a Turbulent Flow Means of a Pitot Tube
34. The Turbulent Velocity Distribution
35. The Turbulent Velocity Distribution in the Region of Transition Near the Entrance of the Tube
36. The Pressure Drop in the Turbulent Region of Transition
37. Convergent and Divergent Flow
CHAPTER IV BOUNDARY LAYERS
38. The Region in Which Viscosity is Effective for Large Reynolds' Numbers
39. The Order or Magnitude of the Various Terms in the Equation of Navier-Stokes for Large Reynolds' Numbers
40. The Differential Equation of the Boundary Layer
41. Definition of Thickness of the Boundary Layer
42. Estimate of the Order of Magnitude of the Thickness of the Boundary Layer for the Flow along a Flat Plate
43. Skin Friction Due to a Laminar Boundary Layer
44. Back Flow in the Boundary Layer as the Cause of Formation of Vortices
45. Turbulent Boundary Layers
46. The Seventh-root Law of the Turbulent Velocity Distribution
47. Shear Stress at the Wall in the Case of a Turbulent Boundary Layer and the Thickness of This Layer
48. Friction Drag Due to a Turbulent Boundary Layer
49. Laminar Boundary Layer Inside a Turbulent one
50. Means of Avoiding the Creation of Free Vortex Sheets and Their Consequences
51. Influencing the Flow by Sucking Away the Boundary Layer
52. Rotating Cylinder and Magnus Effect
CHAPTER V DRAG OF BODIES MOVING THROUGH FLUIDS
53. Fundamental Notions
54. Newton's Resistance Law
55. Modern Ideas on the Nature of Drag
56. The Deformation Resistance for Very Small Reynolds' Numbers
57. The Influence of a Very Small Viscosity on the Drag
58. The Relative Importance of Pressure Drag and Friction Drag with Various Shapes of the Body
59. The Variation of the Drag with Reynolds' Number
60. "The Laws of Pressure Drag, Friction Drag, and Deformation Drag"
61. General Remarks on the Experimental Results
62. The Relation c = f (R) for the Infinite Cylinder
63. The Region above the Critical Reynolds' Number
64. "The Resistance Law for Finite Cylinders, Spheres, and Streamlines Bodies"
65. Resistance in Fluids with Free Surfaces; Wave Resistance
66. The General Resistance Law
67. Resistance to Potential Flow
68. Drag of a Sphere Is Zero for Uniform Potential Flow
69 Resistance Due to Acceleration
70. Application of the Momentum Theorem
71. Mutual Forces between Several Bodies Moving through a Fluid
72. Resistance with Discontinuous Potential Flow
73. Stoke's Law of Resistance
74. Experimental Verification for Water; Influence of the Walls of the Vessel
75. Experimental Verification for Gases
76. Correction of Stoke's Law by Oseen
77. The Resistance of Bodies in Fluids of Very Small Viscosity
78. The Resistance of the Half Body
79. Momentum of a Source
80. The Resistance of a Body Calculated from Momentum Considerations
81. Method of Betz for the Determination of the Drag from Measurements in the Wake
82. The Kármán Trail
83. Application of the Momentum Theorem to the Kármán Trail
84. Bodies of Small Resistance; Streamlining
85. Comparison of the Calculated Pressure Distribution with the Experimental One
86. Friction Drag of Flat Plates
CHAPTER VI AIRFOIL THEORY
A. Experimental Results
87. Lift and Drag
88. The Ratio of Lift to Drag; Gliding angle
89. The Lift and Drag Coefficients
90. The Polar and Moment Diagrams of an Airfoil
91. Relation between the Flying Characteristics of Airfoils and Their Pofiles
92. Properties of Slotted Wings
93. The Principle of Operation of a Slotted Wing
94. Pressure Distribution on Airfoils
B. The Airfoil of Infinite Length (Two-dimensional Airfoil Theory)
95. Relation beween Lift and Circulation
96. The Pressure Integral over the Airfoil Surface
97. Derivation of the Law of Kutta-Joukowsky by Means of the Flow through a Grid
98. Derivation of the Lift Formula of Kutta-Joukowsky on the Assumption of a Lifting Vortex
99. The Generation of Circulation
100. The Starting Resistance
101. The Velocity Field in the Vicinity of the Airfoil
102. Application of Conformal Mapping to the Flow round Flat or Curved Plates
103. Superposition of a Parallel Flow and a Circulation Flow
104. Determination of the Amount of Circulation
105. Joukowsky's Method of Conformal Mapping
106. Mapping of Airfoil Profiles with Finite Tail Angle
C. Three-dimensional Airfoil Theory
107. Continuation of the Circulation of the Airfoil in the Wing-tip Eddies
108. Transfer of the Airplane Weight to the Surface of the Earth
109. Relation between Drag and Aspect Ratio
110. Rough Estimate of the Drag
111. The Jump in Potential behind the Wing
112. The Vortex Sheet behind the Wing with Lift Tapering toward the Tips
113. The Downward Velocity Induced by a Single Vortex Filament
114. Determination of the Induced Drag for a Given Lift Distribution
115. Minimum of the Induced Drag; the Lift Distribution of an Airfoil of Given Shape and Angle of Attack
116. Conversion Formulas
117. Mutual Influence of Bound Vortex Systems; the Unstaggered Biplane
118. The Staggered Biplane
119. The Total Induced Drag of Biplanes
120. Minimum Theorem for Multiplanes
121. The Influence of Walls and of Free Boundaries
122. Calculation of the Influece for a Circular Cross Section
CHAPTER VII EXPERIMENTAL METHODS AND APPARATUS
A. Pressure and Velocity Measurements
123. General Remarks on Pressure Measurement in Liquids and Gases
124. Static Pressure
125. Total Pressure
126. Velocity Measurement with Pitot-static Tube
127. Determination of the Direction of the Velocity
128. Fluid Manometers
129. Sensitive Pressure Gages
130. Vane Wheel Instruments
131. Electrical Methods of Velocity Measurement
132. Velocity Measurements in Pipes and Channels
133. Venturi Meter
134. Orifices
135. Weirs
136. Other Methods for Volume Measurement
B. Drag Measurements
137. The Various Methods
138. Towing Tests
139. The Method of Free Falling
140. Rotating-arm Measurements
141. Drag Measurement in the Natural Wind
142. Advantages of Drag Measurement in an Artificial Air Stream
C. Wind Tunnels
143. The First Open Wind Tunnels of Stanton and Raibouchinsky
144. The First Closed Wind Tunnels in Göttingen and London
145. The First Wind Tunnel of eiffel with Free Jet
146. Modern English Tunnels
147. The Large Wind Tunnel in Göttingen
148. Wind Tunnels in Other Countries
149. Suspension of the Models and Measurement of the Forces
150. The Three-component Balance in Göttingen
151. The Aerodynamic Balance of Eiffel
D. Visualizing Flow Phenomena
152. Fundamental Difficulties
153. Mixing Smoke in air Streams
154. Motions in the Boundary Layer
155. Three-dimensional Fluid Motions
156. Two-dimensional Fluid Motions
157. Advantage of Photographs over Visual Observations
158. Streamlines and Path Lines
159. Slow and Fast Moving Pictures
160. Long-exposure Moving Pictures
161. Technical Details
PLATES
INDEX