Hi, when I analyze the small sphere fall in still water with acceleration, is there a suitable equation to illustrate its relaxation time on the sphere velocity? Thank you in advance!
Dear Zegao,
If you mean the settling velocity of the ball, according to Newtons , Archimedes and Stokes laws
V = 2 (particle density _ fluid density ) gravity *particle radius ^ 2 /(9 *fluid viscosity )
Dear Zegao,
It's easy to derive that equation. Please see the attachment.
Regards
Aimen
A possible better equation about the relaxation time can be found in the attachment, considering the effect of the densities of fluid and sphere, sphere diameter, fluid kinematic viscosity, and sphere Reynolds number. However, the initial velocity effect of the sphere was neglected.
Dear Zegao,
Actually I could not catch the relation between your first question and your attachement! In your first question you mentioned that you are working on a analysing a single small sphere falls in still water. While the attachement talks about the moving of a small sphere in turbulent gas flow considering the particle _particle intercollision effect!
Propably I could not understand your original question!
Yours
Dear Aimen Zeiny,
Thanks a lot for your kind reply.In these days, I am always looking for a suitable equation for the acceleration fall of a sphere in still water. So I looked around the reference by accident. I would understand the reference and your recommended equation in details.
Best regards,
Zegao
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