Sometimes, we are more concerned with how much mechanical energy has been converted into internal energy (or how much mechanical energy has been lost) during a flow process. The strong shear flow inside the boundary layer results in mechanical energy losses whose magnitude depends directly on the magnitudes of shear force and shear rate, amd and mechanical energy loss corresponds to energy thickness. We can define the energy thickness in a similar way as the displacement thickness

$$ \delta_{3}=\int_{0}^{\infty}\frac{u}{U}\left(1-\frac{u^{2}}{U^{2}}\right)\,dy $$ The energy thickness $\delta_{3}$ is the distance by which the boundary should be displaced to compensate for the deficit in kinetic energy of the free flow caused by the boundary layer