A third measure of the boundary-layer thickness is the momentum thickness $\theta$ or $\delta_2$. It is defined such that $\rho U^2 \theta$ is the momentum loss in the actual flow because of the presence of the boundary layer

A control volume calculation leads to the following definition $$ \theta=\int_{y=0}^{\infty}\frac{u}{U_e}\left(1-\frac{u}{U_e}\right)\,dy $$

The momentum thickness embodies the integrated influence of the wall shear stress from the beginning of the boundary layer to the stream-wise location of interest