Short Notes: Boundary Layer | Short Notes for Mechanical Engineering PDF Download

 Page 1


Boundary Layer 
Boundary layer phenomenon occurs when a fluid flows over a flat plate causing 
laminar or turbulent flow. This topic defines various parameters such as Energy 
thickness, Momentum thickness, Boundary layer thickness etc.
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
du 
ay
will exist.
Note: velocity gradient
du
dy
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
f*
For laminar boundary layer
(Re)x < 5 x 1 o5 (For flat plate) and if (Re)x > 5 x 1 o5
where R e = Reynold number
Then, flow is turbulent.
Page 2


Boundary Layer 
Boundary layer phenomenon occurs when a fluid flows over a flat plate causing 
laminar or turbulent flow. This topic defines various parameters such as Energy 
thickness, Momentum thickness, Boundary layer thickness etc.
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
du 
ay
will exist.
Note: velocity gradient
du
dy
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
f*
For laminar boundary layer
(Re)x < 5 x 1 o5 (For flat plate) and if (Re)x > 5 x 1 o5
where R e = Reynold number
Then, flow is turbulent.
Here, x is distance from leading edge in horizontal direction.
Boundary Layer Thickness (5): 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 5.
Boundary Layer thickness 8
Displacement Thickness (5*): 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 (5*).
Page 3


Boundary Layer 
Boundary layer phenomenon occurs when a fluid flows over a flat plate causing 
laminar or turbulent flow. This topic defines various parameters such as Energy 
thickness, Momentum thickness, Boundary layer thickness etc.
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
du 
ay
will exist.
Note: velocity gradient
du
dy
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
f*
For laminar boundary layer
(Re)x < 5 x 1 o5 (For flat plate) and if (Re)x > 5 x 1 o5
where R e = Reynold number
Then, flow is turbulent.
Here, x is distance from leading edge in horizontal direction.
Boundary Layer Thickness (5): 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 5.
Boundary Layer thickness 8
Displacement Thickness (5*): 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 (5*).
X
Plate
Boundary layer displacement thickness (5‘)
Momentum Thickness (0): 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 (5**): 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
, . _ . du
(a) A ty =0.u = 0. — = 0
dy
(b) A ty = 6.u = U.— = 0
dy
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.
If Re = - < 2000
M
Where, p = Density of fluid, v = Velocity of fluid, D = Diameter of pipe, p = Viscosity 
of fluid.
For flat plate flow will be laminar.
If Re = .^— -< 5 x l0 5 
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 x 1 o5.
Von Karman Momentum Integral Equation
rc dd
pU‘ dx
Page 4


Boundary Layer 
Boundary layer phenomenon occurs when a fluid flows over a flat plate causing 
laminar or turbulent flow. This topic defines various parameters such as Energy 
thickness, Momentum thickness, Boundary layer thickness etc.
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
du 
ay
will exist.
Note: velocity gradient
du
dy
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
f*
For laminar boundary layer
(Re)x < 5 x 1 o5 (For flat plate) and if (Re)x > 5 x 1 o5
where R e = Reynold number
Then, flow is turbulent.
Here, x is distance from leading edge in horizontal direction.
Boundary Layer Thickness (5): 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 5.
Boundary Layer thickness 8
Displacement Thickness (5*): 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 (5*).
X
Plate
Boundary layer displacement thickness (5‘)
Momentum Thickness (0): 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 (5**): 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
, . _ . du
(a) A ty =0.u = 0. — = 0
dy
(b) A ty = 6.u = U.— = 0
dy
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.
If Re = - < 2000
M
Where, p = Density of fluid, v = Velocity of fluid, D = Diameter of pipe, p = Viscosity 
of fluid.
For flat plate flow will be laminar.
If Re = .^— -< 5 x l0 5 
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 x 1 o5.
Von Karman Momentum Integral Equation
rc dd
pU‘ dx
where, 0 = momentum thickness 
Shear stress:
Where, U = Free stream velocity; p = Density of fluid.
Local Coefficient of Drag (C*D ):
It is defined as the ratio of the shear stress t0 to the quantity
It is denoted by
Average Coefficient of Drag (CD ):
It is defined as the ratio of the total drag force to
Where, A = Area of surface, U = Free stream velocity, p = Mass density of fluid. 
Total drag on a flat plate due to laminar and turbulent boundary layer:-
Total darg= Laminar drag upto tansition boundary+ turbulent drag for whole plate-
turbulent drag upto transition boundary
Drag force=FD = V 2 p * v2 * CD * A
Blassius Experiment Results
For laminar flow,
/ 4.91
Coefficient of drag
Page 5


Boundary Layer 
Boundary layer phenomenon occurs when a fluid flows over a flat plate causing 
laminar or turbulent flow. This topic defines various parameters such as Energy 
thickness, Momentum thickness, Boundary layer thickness etc.
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
du 
ay
will exist.
Note: velocity gradient
du
dy
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
f*
For laminar boundary layer
(Re)x < 5 x 1 o5 (For flat plate) and if (Re)x > 5 x 1 o5
where R e = Reynold number
Then, flow is turbulent.
Here, x is distance from leading edge in horizontal direction.
Boundary Layer Thickness (5): 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 5.
Boundary Layer thickness 8
Displacement Thickness (5*): 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 (5*).
X
Plate
Boundary layer displacement thickness (5‘)
Momentum Thickness (0): 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 (5**): 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
, . _ . du
(a) A ty =0.u = 0. — = 0
dy
(b) A ty = 6.u = U.— = 0
dy
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.
If Re = - < 2000
M
Where, p = Density of fluid, v = Velocity of fluid, D = Diameter of pipe, p = Viscosity 
of fluid.
For flat plate flow will be laminar.
If Re = .^— -< 5 x l0 5 
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 x 1 o5.
Von Karman Momentum Integral Equation
rc dd
pU‘ dx
where, 0 = momentum thickness 
Shear stress:
Where, U = Free stream velocity; p = Density of fluid.
Local Coefficient of Drag (C*D ):
It is defined as the ratio of the shear stress t0 to the quantity
It is denoted by
Average Coefficient of Drag (CD ):
It is defined as the ratio of the total drag force to
Where, A = Area of surface, U = Free stream velocity, p = Mass density of fluid. 
Total drag on a flat plate due to laminar and turbulent boundary layer:-
Total darg= Laminar drag upto tansition boundary+ turbulent drag for whole plate-
turbulent drag upto transition boundary
Drag force=FD = V 2 p * v2 * CD * A
Blassius Experiment Results
For laminar flow,
/ 4.91
Coefficient of drag
Average coefficient of drag
1.328
For turbulent flow,
/ _ 0-37
x -
(Re,)5
where x = Distance from leading edge Rex = Reynold number for length x. 
Rex = Reyonold number at end of plane 
Coefficient of drag
_ 0.059
'-ft ~ i
( RV )?
Average coefficient of drag
( Re£ )5
For laminar flow
focyfx
f = Boundary layer thickness,
1
t o = Shear stress at solid surface 
x = Distance from where solid surface starts. 
Velocity profile for turbulent boundary layer is
u
U
L
/ ,
l
n
1
=¦5x10- < Re <107
Conditions for Boundary Layer Separation: Let us take curve surface ABCSD where 
fluid flow separation print S is determined from the condition