Sunday, 28 April 2019

fluid dynamics - Stokes law in 2-dimensions


Stokes' law states that force on slow moving sphere (i.e. Re1) in liquid is Fd=6πμRV



In two dimensions we are in trouble (flow around disk in 2d or around cylinder in 3d), because there is no solution to the Stokes' problem (known as Stokes' paradox), but from dimensional analysis we can still conclude that


Fd=CμV


I did some numerical tests of Navier-Stokes equations for small Reynolds numbers and found that Fd really does not depend on R and C4π.


I find it quite counter-intuitive that the force in 2D does not depend on the disk radius. Have I done something wrong? Or it really does not depend on radius of the disk?


Only thing which depends on the disk radius is the admissible range of input velocities. If you increase R than you have to lower the max V to ensure the condition Re1.




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