Submerged Landau jet

Question

I am reading Landau & Lifshitz's Fluid Mechanics. On page 81, section 23, it reads

Determine the flow in a jet emerging from the end of a narrow tube into an infinite space filled with the fluid - the submerged jet. We take spherical polar coordinates $r,\theta,\phi$, with the polar axis in the direction of the jet at its point of emergence, and with this point as origin. The flow is symmetrical about the polar axis, so that $v_\phi=0$ and $v_\theta,v_r$ are functions of $r$ and $\theta$ only. The same total momentum flux (the "momentum of the jet") must pass through any closed surface surrounding the origin (in particular, through an infinitely distant surface). For this to be so, the velocity must be inversely proportional to $r$, so that $$v_r=F(\theta)/r, v_\theta=f(\theta)/r, \tag{23.16}$$ where $F$ and $f$ are some functions of $\theta$ only.

I don't know how $(23.16)$ is derived. Can someone explain it?