Taylor scraping flow: Difference between revisions

Revision as of 03:02, 7 November 2020

Revision as of 11:13, 17 February 2021

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:<math>\sigma_t = \frac{2\mu U}{r} \frac{\sin\alpha-\alpha\cos\alpha}{\alpha^2 - \sin^2\alpha}, \quad \sigma_n =\frac{2\mu U}{r} \frac{\alpha\sin\alpha}{\alpha^2 - \sin^2\alpha} </math>

The same scraper stress if resolved according to Cartesian coordinates (parallel and perpendicular to the lower plate i.e. <math>\sigma_x = -\sigma_t \sincos\alpha + \sigma_n \cossin\alpha, \ \sigma_y = -\sigma_t \cossin\alpha + \sigma_n \sincos\alpha</math>) are

:<math>\sigma_x = \frac{2\mu U}{r} \frac{\alpha-\sin\alpha\cos\alpha}{\alpha^2 - \sin^2\alpha}, \quad \sigma_y =\frac{2\mu U}{r} \frac{\sin^2\alpha}{\alpha^2 - \sin^2\alpha} </math>