Past exam of the mathematics course of the University of Cambridge / 2015 / ii / Paper 3 / 36E / i

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 the boundary-layer equationThe radial velocity is small but its convective term is of the same order as axial convection because radial gradients are larger.