# Boundary layer theory

1. Nov 9, 2014

### mrajkumar

Hi,
could you tell the physical meaning of the displacement and momentum thickness of a boundary layer.And why the stream line diverges away from the body in the boundary layer to conserve mass?

2. Nov 14, 2014

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Nov 19, 2014

### rcgldr

update - I wan't sure about what you meant by momentum thickness, but thanks to boneh3ad's next post, it's explained there.

flat plate.htm

Last edited: Nov 19, 2014
4. Nov 19, 2014

The displacement thickness ($\delta_1$ or $\delta^*$) is a measure of the effect of the boundary layer on the flow of mass in a fluid. Essentially, you can solve the flow inviscidly and come up with a certain overall mass flow rate. Then solve the same flow accounting for the boundary layer, and the mass flow will be slightly smaller. The displacement thickness is the distance the surface would have to be displaced in order that the mass flow in the inviscid case would be the same as that in the viscous case with the original wall position. In essence, it is the distance the wall must move in order to get the same outer flow (inviscid) answer without solving for the boundary layer.
$$\delta^* = \int\limits_0^{\infty}\left(1 - \dfrac{u}{U_{\infty}}\right)dy.$$
The momentum thickness ($\delta_2$ or $\theta$) is similar, only it deals with the flow of momentum rather than mass. It shows up in the momentum integral boundary layer equation (as does $\delta^*$).
$$\theta = \int\limits_0^{\infty}\dfrac{u}{U_{\infty}}\left(1 - \dfrac{u}{U_{\infty}}\right)dy$$