##### Let’s assume a fluid is flowing over a solid body.**When a real fluid flows over a solid body, the velocity of fluid at the boundary will be zero.**

##### As we move away from boundary in perpendicular direction velocity increases to the free stream velocity i.e. there will be velocity gradient.

As we can see in the figure fluid is flowing over the solid surface. So u = u_∞ is the free stream velocity which will be perpendicular to boundary layer.

u = 0 over the surface and δ (boundary layer thickness) is the thickness between Free stream and surface.

**Development of Boundary Layer**

Development of boundary layer can be categorized in three regions

- Laminar
- Transition
- Turbulent

A fluid is determined as laminar or turbulent with the help of Reynolds number (Re), which is given by

Where, ρ = density of fluid

v = velocity of fluid

x = distance from leading edge in horizontal direction

μ = viscosity of fluid

**1. Boundary layer thickness (δ)**

It is the distance from the surface of the solid body to the point where velocity of fluid is approximately equal to 99% of free stream velocity. It is denoted by δ

**2. Displacement thickness (δx)**

It is observed that inside the boundary layer velocity of the fluid is less than free stream velocity hence, discharge is less in this region.

To compensate for the reduction in discharge the boundary is displaced outward in the perpendicular direction by some distance. This distance is called displacement thickness (δx)

Let’s find out an expression of displacement thickness.

**3. Momentum thickness (θ)**

Due to boundary layer reduction in velocity occurs so, momentum also decreases, Momentum thickness is defined as the distance measured normal to the boundary of a solid body by which the boundary should be displaced to compensate for the reduction in momentum of flowing fluid.

**4. Energy thickness (δxx)**

It is defined as the distance measured perpendicular to the boundary of the solid body, by which the boundary should be displaced to compensate for the reduction in kinetic energy of flowing fluid. (Kinetic energy decreases due to the formation of boundary layer)

**Boundary conditions for velocity profile**