Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

Mechanical Engineering SSC JE (Technical)

Mechanical Engineering : Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

The document Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev is a part of the Mechanical Engineering Course Mechanical Engineering SSC JE (Technical).
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BOUNDARY LAYER THEORY

  •  The concept of boundary layer was first introduced by L. Prandt in 1904. 
  • Boundary layer is a region in the immediate vicinity of the boundary surface in which the velocity of flowing fluid increases gradually from zero at the boundary surface to the velocity of the main stream.

Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

  • Boundary Conditions of Boundary Layer Region 
    (i) at y = 0, v = 0
    (ii) at y = d, v = V0 (d = boundary layer thickness V0 = free stream velocity)
    (iii) at y = d, Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev = 0 [∵ Q v = V0 = constant]
    (iv) 
    Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev
     
  • Boundary layer thickness (d) It is defined as the distance from the boundary surface in which the velocity reaches the 99% of the velocity of the main stream.
    y =d
    for v = 0.99 V
  • Displacement Thickness (d*) It is the distance measured normal to the boundary, by which the free stream is displaced on account of the formation of boundary layer.
    Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev
    The quantity (V0 – v) is known as the velocity defect.
  •  Momentum Thickness (q)

Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

The ratio of displacement thickness to momentum thickness is called the shape factor (H)

Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

  • Its value should always greater than 1 
     
  • Energy Thickness
    Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

  •  Von-Korman momentum integral equation
    Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev
  •  Blassius experimental results/ when  
    • Laminar Conditions : Velocity distribution is parabolic
      (i) Boundary Layer thickness

      Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev
      (ii) Local coefficient of drag C*D
      Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

      (iii) Avg. Coefficient CD
      Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev
  •  Turbulent Conditions : Velocity distributions is logarithmic
    (i) 
    Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev
    (ii)
    Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev
    (iii)
    Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev
    Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

where
d = Boundary layer thickness
t = Shear stress at solid surface
x = Distance from where solid surface starts 

  • Boundary Layer Separation It is caused by adverse pressure gradient

Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev
Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

  • Location of Separation point : The separation point S is determined from the condition
    Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev
    For a given velocity it can be determined whether the B.L.(Boundary layer) has separated or on the verge of separation or will not separate from the following conditions :

1.
Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev
< 0 : Flow has separated.

2.
Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev
= 0 : Flow is on verge of separation.

3.
Chapter 9 Boundary Layer Theory - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev
0 : Flow is attached with the surface

 

  •  Methods of Preventing Separation
    (i) Rotating the boundary in the direction of flow.
    (ii) Suction of the slow moving fluid by a suction slot.
    (iii) Supplying additional energy from a blower.
    (iv) Providing a bypass in the slotted wing.
    (v) Providing guide blades in a bend.
    (vi) Injecting fluid into boundary layer.
    (vii)Streamlining of body shapes.
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