Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

Document Description: Boundary Layer Theory for Mechanical Engineering 2022 is part of Mechanical Engineering SSC JE (Technical) preparation. The notes and questions for Boundary Layer Theory have been prepared according to the Mechanical Engineering exam syllabus. Information about Boundary Layer Theory covers topics like and Boundary Layer Theory Example, for Mechanical Engineering 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Boundary Layer Theory.

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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.

Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

  • 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, Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering = 0 [∵ Q v = V0 = constant]
    (iv) 
    Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
     
  • 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.
    Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
    The quantity (V0 – v) is known as the velocity defect.
  •  Momentum Thickness (q)

Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

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

Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

  • Its value should always greater than 1 
     
  • Energy Thickness
    Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

  •  Von-Korman momentum integral equation
    Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
  •  Blassius experimental results/ when  
    • Laminar Conditions : Velocity distribution is parabolic
      (i) Boundary Layer thickness

      Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
      (ii) Local coefficient of drag C*D
      Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

      (iii) Avg. Coefficient CD
      Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
  •  Turbulent Conditions : Velocity distributions is logarithmic
    (i) 
    Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
    (ii)
    Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
    (iii)
    Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
    Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

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

Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

  • Location of Separation point : The separation point S is determined from the condition
    Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
    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.
Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
< 0 : Flow has separated.

2.
Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
= 0 : Flow is on verge of separation.

3.
Boundary Layer Theory Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
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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