Boundary Layer Theory

By Deepanshu Rastogi|Updated : October 21st, 2021

This article contains basic notes on the "Boundary Layer Theory"  topic of the "Fluid Mechanics & Hydraulics" subject.    

This article contains basic notes on the "Boundary Layer Theory"  topic of the "Fluid Mechanics & Hydraulics" subject.

Boundary-Layer Theory

Boundary Layer Theory

When a real fluid flows over a solid body, the velocity of fluid at the boundary will be zero. If boundary is stationary. As we move away from boundary in perpendicular direction velocity increases to the free stream velocity. It means velocity gradient image001 will exist.


Velocity gradient image002 does not exist outside the boundary layer as outside the boundary layer velocity is constant and equal to free stream velocity.

Development of Boundary Layer: Development of boundary layer can be divided in three regions: laminar, transition, turbulent.

Reynolds number


For laminar boundary layer

(Re)x < 5 × 105 (For flat plate) and if (Re)x > 5 × 105

where Re = Reynolds's number

Then, flow is turbulent.



Here, x is distance from leading edge in horizontal direction.

Boundary Layer Thickness (δ): It is the distance from the boundary to the point where velocity of fluid is approximately equal to 99% of free stream velocity. It is represented by δ.


Displacement Thickness (δ*): It is observed that inside the boundary layer velocity of fluid is less than free stream velocity hence, discharge is less in this region. To compensate for reduction in discharge the boundary is displaced outward in perpendicular direction by some distance. This distance is called displacement thickness (δ*).



Momentum Thickness (θ): As due to boundary layer reduction in velocity occurs so, momentum also decreases. Momentum thickness is defined as the distance measured normal to boundary of solid body by which the boundary should be displaced to compensate for the reduction in momentum of flowing fluid.


Energy Thickness (δ**): It is defined as distance measured perpendicular to the boundary of solid body by which the boundary should be displaced to compensate for reduction in kinetic energy of flowing fluid (KE decreases due to formation of boundary layer)


Boundary Conditions for the Velocity Profile: Boundary conditions are as



Laminar Flow: A flow in which fluid flows in layer and no intermixing with each other is known as laminar flow. For circular pipe, flow will be laminar.


Where, ρ = Density of fluid, v = Velocity of fluid,

D = Diameter of pipe, μ = Viscosity of fluid.

For flat plate flow will be laminar.


Where L is length of plate.

Turbulent Flow:

In this flow, adjacent layer of fluid cross each other (particles of fluid move randomly instead of moving in stream line path), for flow inside pipe. If Re > 4000, the flow is considered turbulent, for flat plate, Re > 5 × 105.

Von Karman Momentum Integral Equation


where, θ = momentum thickness

Shear stress: image016

Where, U = Free stream velocity; ρ = Density of fluid.

Local Coefficient of Drag (CD*):

It is defined as the ratio of the shear stress τ0 to the quantity image017

It is denoted by image018

Average Coefficient of Drag (CD):

It is defined as the ratio of the total drag force to image019


Where, A = Area of surface,

U = Free stream velocity, ρ = Mass density of fluid.

Blassius Experiment Results

For laminar flow,


Coefficient of drag


Average coefficient of drag


For turbulent flow, image024 

where x = Distance from leading edge, Rex = Reynolds's number for length x.

ReL = Reynolds's number at end of plate

Coefficient of drag



Average coefficient of drag


For laminar flow


f = Boundary layer thickness,


τ0 = Shear stress at solid surface

x = Distance from where solid surface starts.

Velocity profile for turbulent boundary layer is


Conditions for Boundary Layer Separation: Let us take curve surface ABCSD where fluid flow separation print S is determined from the condition image030.


If image032 

the flow is separated image033

If image034 

the flow is on the average of separation


If image036 the flow will not separate or flow will remain attained image037

Methods of Preventing Separation of Boundary Layer: Suction of slow-moving fluid by a suction slot.

  • Supplying additional energy from a blower.
  • Providing a bypass in the slotted
  • Rotating boundary in the direction of flow.
  • Providing small divergence in a diffuser.
  • Providing guide blades in a bend.
  • Providing a trip wire ring in the laminar region for the flow over a sphere.

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All the Best

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Deepanshu RastogiDeepanshu RastogiMember since Jul 2020
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Ansari Jawed

Ansari JawedSep 22, 2016

Thanks a lot sir
Himanshu Pandey
Please sir I need manometry concepts. Thanks
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Can anybody provide me rk Bansal book (fluid mechanics )pdf????

YogiAug 20, 2019

Thsnku very much sir its helpfull to quick revision
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