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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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Chapter 9

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, = 0 [∵ Q v = V₀ = constant]
(iv)
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 V₀
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.

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

 Von-Korman momentum integral equation
Blassius experimental results/ when 
- Laminar Conditions : Velocity distribution is parabolic
  (i) Boundary Layer thickness
  
  (ii) Local coefficient of drag C*_D
  
  (iii) Avg. Coefficient C_D
 Turbulent Conditions : Velocity distributions is logarithmic
(i)

(ii)

(iii)

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

Location of Separation point : The separation point S is determined from the condition

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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