# Submerged Landau jet

+ 1 like - 0 dislike
31 views

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?

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysicsOverf$\varnothing$owThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.