= Solution
In a steady <axisymmetric flow> without swirl, time derivatives and azimuthal derivatives vanish. For a slender high-<Reynolds number> jet of width $\delta\ll z$, radial viscous derivatives dominate axial ones by $(z/\delta)^2$. The transverse momentum balance makes pressure nearly constant across the jet, matching the constant ambient pressure, so the leading axial pressure gradient vanishes. Retaining axial convection and radial diffusion in the <Navier-Stokes equation> gives \b[the boundary-layer equation]
$$
\boxed{u_r\partial_ru_z+u_z\partial_zu_z=\frac\nu r\partial_r(r\partial_ru_z).}
$$
The radial velocity is small but its convective term is of the same order as axial convection because radial gradients are larger.
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