1. VII. Analysis of Potential Flows

2. Contents 1. Preservation of Irrotationality 2. Description of 2D Potential Flows 3. Fundamental Solutions 4. Superposition

3. 1. Preservation of Irrotationality

4. Stokes Theorem S C Vorticity Circulation

5. In the flow of an ideal fluid with constant density, circulation along a fluid line is invariant if body force is conservative Kelvin ’ s Theorem

10. fluid is always irrotational if it is initially irrotational A piece of fluid is always irrotational if it is initially irrotational

11. 2. Description of 2D Potential Flows

12. 2D Flow in x-y plane

13. Basic Equations for 2D Potential Flows

14. Velocity Potential

15. Irrotational flow Definition of Velocity Potential

16. Continuity Equation

17. Stream Function

18. Incompressible fluid Definition of Stream Function

19. Irrotational condition

20.  = constant represents a streamline Properties of Stream Function

25. Streamlines and equipotential lines are always perpendicular to each other Properties of Stream Function

27. Along a streamline

28. Along an equipotential line

30. Complex Potential

31. Cauchy-Riemann Condition

32. Analytic Function

33. 3. Fundamental Solutions

34. a. Uniform flow b. Source and sink c. Vortex d. Doublet

35. a. Uniform Flow

40. U

43. b. Source and Sink

44. Source In polar coordinates

49. Discharge

51. Sink

52. Source or Sink at (x 0,y 0 )

53. c. Vortex

54. Vortex In polar coordinates

56. Circulation

58. Clockwise Vortex

59. Vortex centered at (x 0,y 0 )

60. c. Doublet

62. Velocity Potential

63. Stream Function

64. Streamlines

66. 4. Superposition

67. a. Circular Cylinder without Circulation

70. Uniform Flow Doublet

76. On surface of cylinder Velocity

77. 2U Stagnation Point

78. Pressure

80. D’Alembert Paradox

81. Drag due to viscosity ► Skin friction ► Form drag

84. b. Circular Cylinder with Circulation

85. Uniform Flow DoubletVortex

88. On surface of the cylinder

89. Stagnation point on cylinder

90. Pressure

91. Lift