Taylor scraping flow: Difference between revisions

Revision as of 02:54, 7 November 2020

Revision as of 02:56, 7 November 2020

Line 18:

</math>

==Solution==

==Solution<ref>Acheson, David J. Elementary fluid dynamics. Oxford University Press, 1990.</ref>==

Attempting a [[Separation of variables|separable]] solution of the form <math>\psi =U r f(\theta)</math> reduces the problem to

Line 28:

:<math>f(0)=0,\ f'(0)=-1, \ f(\alpha)=0, \ f'(\alpha)=0</math>

The solution is<ref>{{cite book |last=Acheson |first=David J. |title=Elementary Fluid Dynamics |publisher=Oxford University Press |year=1990 |isbn=0-19-859660-X }}</ref>

The solution is

:<math>f(\theta) = \frac{1}{\alpha^2 - \sin^2\alpha} [\theta \sin \alpha \sin (\alpha-\theta) - \alpha(\alpha-\theta) \sin\theta]</math>