Based on the famous series of lectures given at Gottingen by Professor Prandtl and enlarged with additional material on experimental methods by O. G. Tietjens, this volume presents practical applications of theoretical hydro- and aeromechanics. The methods it deals with can easily be followed by engineers, although advanced mathematics is used in the sections on airfoil.

Coverage is wide, ranging from an introduction to flow in pipes to Dr. Prandtl's own work on boundary layers, drag, airfoil theory, and experimental methods. Of special interest are discussions of entry conditions for flow in a pipe; turbulent flow in pipes and in the boundary layer; the method of determining the drag of a body from the velocity and pressure of the wake; measurement of pressure drop at the transition between laminar and turbulent flow; the laws of pressure drag, friction drag, and deformation drag; application of the momentum theorem to the Karman trail; experiments with the properties of slotted wings; the airfoil of infinite length; three-dimensional airfoil theory; and experimental methods and apparatus (pressure and velocity measurements, drag measurements, wind tunnels, and visualizing flow phenomena).

Coverage is wide, ranging from an introduction to flow in pipes to Dr. Prandtl's own work on boundary layers, drag, airfoil theory, and experimental methods. Of special interest are discussions of entry conditions for flow in a pipe; turbulent flow in pipes and in the boundary layer; the method of determining the drag of a body from the velocity and pressure of the wake; measurement of pressure drop at the transition between laminar and turbulent flow; the laws of pressure drag, friction drag, and deformation drag; application of the momentum theorem to the Karman trail; experiments with the properties of slotted wings; the airfoil of infinite length; three-dimensional airfoil theory; and experimental methods and apparatus (pressure and velocity measurements, drag measurements, wind tunnels, and visualizing flow phenomena).

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 Karman Trail 83. Application of the Momentum Theorem to the Karman 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 Gottingen and London 145. The First Wind Tunnel of eiffel with Free Jet 146. Modern English Tunnels 147. The Large Wind Tunnel in Gottingen 148. Wind Tunnels in Other Countries 149. Suspension of the Models and Measurement of the Forces 150. The Three-component Balance in Gottingen 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