Laminar round jet

A laminar round jet is an axisymmetric momentum-driven flow issuing into otherwise still fluid. Viscous diffusion broadens the jet while its axial momentum flux remains constant.

For axial velocity $w(r,z)$ in the boundary-layer approximation,is independent of $z$. If $W$ and $\delta$ are characteristic centre-line speed and width, then $W\delta \sim M^{1/2}$, while the momentum balance gives $W{\delta }^2\sim \nu z$. Thus

With axisymmetric streamfunction $\psi =\nu zg(r/z)$, the regular normalized similarity profile isIts volume flux grows linearly with $z$, expressing fluid entrainment.