This document defines and compares three types of boundary layer thickness: 1. Boundary layer thickness is the distance from the surface where the flow velocity is 99% of the free-stream velocity. 2. Displacement thickness is a theoretical thickness where displacing the surface would result in equal flow rates across sections inside and outside the boundary layer. 3. Momentum thickness is a measure of boundary layer thickness defined as the distance the surface would need to be displaced to compensate for the reduction in momentum due to the boundary layer. It is often used to determine drag on an object.

1. Displacement Thickness
&
Momentum Thickness
1
Group Members
GC Jabran Naveed
Cheema
GC Haroon ur Rashid
GC Bilal Masood
NS Ashir Azeem

2. A boundary layer is the layer of fluid in the immediate vicinity of a bounding
surface where the effects of viscosity are significant.
Boundary
Layers
2

3. 3
There are three main definitions of boundary layers :
1. Boundary layer thickness
2. Displacement thickness
3. Momentum thickness
Boundary layer equations represent a significant simplification over the full Navier-Stokes
equations in a boundary layer region.
For simplicity, we determine equations for steady, incompressible, uniform flow over a flat
plate. The equations for flow over curved surfaces, and for non-uniform flow, differ only
slightly. The equations for compressible boundary layers are somewhat more complex than
the incompressible equations; we will not consider them here.

4. 4
Assumptions
The boundary layer equations require several assumptions about the flow in the boundary layer.
1. All of the viscous effects of the flow field are confined to the boundary layer, adjacent to the wall .
Outside of the boundary layer, viscous effects are not important, so that flow can be determined by in viscid
solutions such as potential flow or Euler equations.
2.The viscous layer is thin compared to the wall.
3.The boundary conditions of the boundary layer region are the no-slip condition at the wall, and the free-
stream condition at infinity:

5.  δ(x) is the boundary layer thickness when u(y) =0.99V
 V is the free-stream velocity
 The purpose of the boundary layer is to allow the fluid to change its
velocity from the upstream value of V to zero on the surface
5Boundary Layer Thickness

6.  There is a reduction in the flow
rate due to the presence of the
boundary layer
 This is equivalent to having a
theoretical boundary layer with
zero flow
Displacement Thickness 6

7. Mathematically
:
Because of the velocity deficit, within the boundary layer, the flow rate across
section b–b is less than that across section a–a. However, if we displace the plate at
section a–a by an appropriate amount the boundary layer displacement thickness,
the flow rates across each section will be identical.
7
Where b is plate width

8. Momentum Thickness 8
 Momentum thickness is a measure of the boundary layer thickness.
 It is defined as the distance by which the boundary should be displaced to
compensate for the reduction in momentum of the flowing fluid on account of
boundary layer formation
 The momentum thickness, symbolized by Ө is the distance that, when multiplied by the
square of the free-stream velocity, equals the integral of the momentum defect, across the
boundary layer.

9. 9
It is often used when determining the drag on an object. Again because of the
velocity deficit U-u, in the boundary layer, the momentum flux across section b–b in
Fig. 9.8 is less than that across section a–a. This deficit in momentum flux for the
actual boundary layer flow on a plate of width b is given by

10. Mathematically
:
which by definition is the momentum flux in a layer of uniform speed U and thickness
Ө.That is,
10

11. Thank You
11