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- ISBN: 9780486603759 | 048660375X
- Cover: Paperback
- Copyright: 4/19/2012

Prandtl was one of the great theorists of aerodynamics. 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

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