Navier-Stokes in cylindrical coordinates [Fluid Mechanics

A small side video that covers Cylindrical Coordinates. There are many different coordinate systems, the three main being Cartesian, Cylindrical, and Spherical. Cartesian is the most popular, but cylindrical is also common especially in pipe flows. Different coordinate systems are useful for different applications. We will go over why the equations are different for cylindrical coordinates and you will get a new set of incompressible Conservation equations to use in pipe flows.
Free downloadable notes (PDF with white background) can be found at my website: sites.udel.edu...

[@smixit2043]

is there any way you can make a video on deriving the navier stokes equations for each direction in the cylindrical coordinate system ?

[@prof.vanburen]

Ohh good question! I usually avoid it, but you're right it's hard to find a good resource/walkthrough of it. Maybe in the coming months?

[@erfuniti3570]

Thank You. How could I learn about derive Navier-Stokes equation in cylindrical coordinates from Cartesian? Is there any book explained it?@@prof.vanburen

[@priyojeetdash9467]

Sir, is there any way how to remember the NS equation in cylindrical coordinate system?

[@prof.vanburen]

Unfortunately I don't know any useful tricks other than memorizing it completely. Typically the radial derivative terms are a slightly different than the cartesian counterpart, but not always. Just be sure to check units, knowing that and d(.)/dtheta term needs a 1/r with it in order for units to match the other terms.

[@priyojeetdash9467]

Thank you sir, even this helps a lot !

[@drandrewsanchez]

Great video!!

[@prof.vanburen]

Thanks!!

[@heeyoon6099]

Hello, I would like to know compressible coordinate problem. can you explain it to me?

[@prof.vanburen]

Hi! I am not familiar with that particular problem. Do you mean compressible NS in cylindrical coordinates?

[@alixroussaly5125]

@@prof.vanburen yes I'm interested too !

[@bluemantle8269]

How did the polar coordinate became a bread loaf in 3d

[@prof.vanburen]

The "bread loaf" is just anecdotal. You have two arc segments connected by straight lines, and this is extended/extruded linearly in the third direction. This makes a shape that looks similar to a loaf of bread.

[@GoogleAccount-kc6rt]

Thanks ❤

[@prof.vanburen]

No problem!