1. VIII. Viscous Flow and Head Loss

2. Contents 1. Introduction 2. Laminar and Turbulent Flows 3. Friction and Head Losses 4. Head Loss in Laminar Flows 5. Head Loss in Turbulent Flows 6. Head Loss of Steady Pipe Flows 7. Minor Losses 8. Examples

3. 1. Introduction

4. Shear stress due to fluid viscosity

5. D’Alembert Paradox

10. For real fluid flows Head Loss

11. Head Loss:  Losses due to friction  Minor Losses entrance and exit sudden change of cross sections valves and gates bends and elbows ……

12. 2. Laminar and Turbulent Flows

13. Reynolds’ Experiment

14. Laminar Flows: Movement of any fluid particle is regular Path lines of fluid particles are smooth Turbulent Flows: Movement of any fluid particle is random Path lines of fluid particles are affected by mixing

15. Transition from Laminar to Turbulent Flow:  for different fluid  for different diameter of pipe

16. Head Loss due to laminar and turbulent flows

18. Turbulent Flows: Laminar Flows:

19. Critical Condition Reynolds Number

20. 3. Friction and Head Losses

22. Momentum Equation A : area of the cross-section P: wetted perimeter

23. Hydraulic radius

24. Darcy-Weisbach equation

25. 4. Head Loss in Laminar Flows

33. 5. Head Loss in Turbulent Flows

34. Mean flow and fluctuation

36. Basic Equations of Turbulent Flows:

39. Reynolds’ Average

41. Reynolds Stresses

42. Mean flux of horizontal momentum: Equivalent Shear Stress:

43. Reynolds Equations:

45. Theory of Mixing Length

46. Logarithmic Velocity Distribution

47. 6. Head Loss of Steady Pipe Flows

48. Logarithmic Velocity Distribution

49. Logarithmic Overlap Layer

50. Logarithmic Velocity Distribution in a Pipe

51. ViscousTurbulent

52. Viscous sublayer: Turbulent zone: Transition zone:

53. Velocity Distribution in Viscous Sublayer

54. Velocity Distribution in a Pipe

55. Blasius’ 7th-root law Valid for R = 3000  10 5

56. Wall Roughness

57. Hydraulically smooth wall: Roughness height is smaller than the thickness of the viscous sublayer Hydraulically rough wall: Roughness height is larger than the lower boundary of the turbulent zone

58. Hydraulically smooth pipe: Hydraulically rough pipe:

59. Velocity Distribution in a Pipe

60. Mean velocity in hydraulically smooth pipe:

61. Mean velocity in hydraulically rough pipe:

62. Relation among mean velocity, friction velocity and friction factor:

63. Friction factor in hydraulically smooth pipe:

64. Friction factor in hydraulically rough pipe:

65. Experiment of Nikuradse

67. Modified friction factor in hydraulically smooth pipe:

68. Modified friction factor in hydraulically rough pipe:

69. Colebrook Equation:

70. Head loss in hydraulically smooth pipe:

71. Practical pipe: equivalent roughness

73. 7. Minor Losses

74. Head Loss due to Sudden Expansion

75. 12

76. Head Loss due to Sudden Contraction

77. Head Loss at Entrance

78. Head Loss at Bell-Mouthed Entrance

79. Head Loss in Bend

82. 8. An Example