Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

146 submissions , 123 unreviewed
3,953 questions , 1,403 unanswered
4,889 answers , 20,762 comments
1,470 users with positive rep
507 active unimported users
More ...

Solution of linear Navier-Stokes equations in a cylindrical coordinates

+ 0 like - 0 dislike
218 views

Can you advise me please how to solve analytically the linear Navier-Stokes equations in a cylindrical coordinate system. Or share the link please if this solution exists somewhere.

Also there is сontinuity equation

asked Dec 20, 2016 in Theoretical Physics by avenior (0 points) [ revision history ]

This set of differential equation lacks the initial and boundary conditions for its variables $p$ and $\bf{v}$. As there is no time derivative, this set describes a steady flow within some "geometry" - in a pipe, cone, etc., not necessarily with cylindrical symmetry.

In this task a solid ball rotates around Oy with a constant angular velocity and it is streamlined with velocity U on the Ox by flow of liquid. In cylindric coordinates z is Oy.

Maybe there is some symmetry which reduces equations.

The boundary conditions on this photo:

1 Answer

+ 0 like - 0 dislike

I do not know what is the analytical solution is in this case, but it may exist in textbooks. What I know is that there is the pressure difference between co-current and counter-current sides. This pressure difference creates a force acting perpendicularly the body velocity and it is known as a Magnus effect. Football players and tennis players use it. Also, cylindrical tubes (rotors) were installed on some ships. I personally can throw a round stone in water and this stone will first enter the water and then reappear above the surface again (jump out of water).

Maybe you can pick up (guess) a solution from qualitative behaviour and dimensional reasoning.

answered Dec 21, 2016 by Vladimir Kalitvianski (22 points) [ revision history ]
edited Dec 21, 2016 by Vladimir Kalitvianski

Your answer

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):
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$\hbar$ysicsOver$\varnothing$low
Then 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.




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...