Taylor scraping flow: Difference between revisions

Revision as of 17:03, 8 May 2017

Revision as of 17:10, 8 May 2017

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:<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>

As noted earlier, all the stresses become infinite at <math>r=0</math>, because the velocity gradient is infinite there. In real life, there will be a huge pressure at the point of point, which depends on the geometry of the contact. The stresses are shown in the figure as given in the Taylor's original paper.

The stress in the direction parallel to the lower wall decreases as <math>\alpha</math> increases, and reaches it's minimum value <math>\sigma_x = \frac{2\mu U}{r}</math> at <math>\alpha=\pi</math>. Taylor says ''The most interesting and perhaps unexpected feature of the calculations is that <math>\sigma_y</math> does not change sign in the range <math>0<\alpha<\pi</math>. In the range <math>\frac{\pi}{2}<\alpha<\pi</math> the contribution to <math>\sigma_y</math> due to normal stress is of opposite sign to that due to tangential stress, but the latter is the greater. The palette knives used by artists for removing paint from their palettes are very flexible scarpersscrapers. They can therefore only be used at such an angle that <math>\sigma_n</math> is small and as will be seen in the figure this occurs only when <math>\alpha</math> is nearly <math>180^\circ</math>. In fact artists instinctively hold their palette knives in this position.'' Further he adds ''A plasterer on the other hand holds a smoothing tool so that <math>\alpha</math> is small. In that way he can get the large values of <math>\sigma_y/\sigma_x</math> which are needed in forcing plaster from protuberances to hollows.''

==References==