Boundary Layer Theory Civil Engineering (CE) Notes | EduRev

Civil Engineering SSC JE (Technical)

Civil Engineering (CE) : Boundary Layer Theory Civil Engineering (CE) Notes | EduRev

The document Boundary Layer Theory Civil Engineering (CE) Notes | EduRev is a part of the Civil Engineering (CE) Course Civil 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.

Boundary Layer Theory Civil Engineering (CE) 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, dv/dy   = 0 [∵ v = V0 = constant]
Boundary Layer Theory Civil Engineering (CE) 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 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.

Boundary Layer Theory Civil Engineering (CE) Notes | EduRev

The quantity (V– v) is known as the velocity defect.

  • Momentum Thickness (q)

 Boundary Layer Theory Civil Engineering (CE) Notes | EduRev

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

 H = d/q

  •   Its value should always greater than 1
  • Energy Thickness

 Boundary Layer Theory Civil Engineering (CE) Notes | EduRev

  •   Von-Korman momentum integral equation

 Boundary Layer Theory Civil Engineering (CE) Notes | EduRev

  • Blassius experimental results/ when 
  • Laminar Conditions : Velocity distribution is parabolic

(i) Boundary Layer thickness

Boundary Layer Theory Civil Engineering (CE) Notes | EduRev

 (ii) Local coefficient of drag C*D

 Boundary Layer Theory Civil Engineering (CE) Notes | EduRev

 (iii) Avg. Coefficient CD

 Boundary Layer Theory Civil Engineering (CE) Notes | EduRev

  •   Turbulent Conditions : Velocity distributions is logarithmic
    Boundary Layer Theory Civil Engineering (CE) Notes | EduRev
    Boundary Layer Theory Civil Engineering (CE) Notes | EduRev
    Boundary Layer Theory Civil Engineering (CE) 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

 Boundary Layer Theory Civil Engineering (CE) Notes | EduRev
Boundary Layer Theory Civil Engineering (CE) Notes | EduRev

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

Boundary Layer Theory Civil Engineering (CE) 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. If
Boundary Layer Theory Civil Engineering (CE) Notes | EduRev < 0 : Flow has separated.
2. If
Boundary Layer Theory Civil Engineering (CE) Notes | EduRev = 0 : Flow is on verge of separation.
3. If
Boundary Layer Theory Civil Engineering (CE) 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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