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Use the continuity equation to write the axial momentum equation in conservative form:Integrating from the axis to infinity, regularity at $r=0$ and decay of $u,w,w_r$ as $r\to \infty$ eliminate the boundary terms. Therefore the conserved momentum flux of a laminar round jet satisfies

Let $W(z)$ be the centre-line velocity scale and $\delta (z)$ the jet width. Conservation gives $M\sim W^2{\delta }^2$, hence $W\delta \sim M^{1/2}$. The axial inertial and viscous terms scale asso $W{\delta }^2\sim \nu z$. Combining the two relations givesThus the width grows linearly and the centre-line speed decays as $z^{-1}$. The volume flux scales asso it increases downstream. By fluid entrainment, the extra flux must be ambient fluid drawn radially into the jet.