Kinetic energy flux of a uniform jet ($\dot{K}=\rho A{u}^3/2$)

A steady uniform incompressible jet has mass flow rate $\rho Au$, momentum flux $\rho A{u}^2$ and kinetic-energy flux $\rho A{u}^3/2$. These use the area and velocity at the same cross section. A nonuniform profile instead requires integrating powers of local speed; using mean speed in a cubic flux without a profile correction is generally wrong.