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:<math>p(r,\theta) - p_\infty = \frac{2\mu U}{r} \frac{\alpha\sin\theta+\sin\alpha\sin(\alpha-\theta)}{\alpha^2 - \sin^2\alpha} </math>
==Forces on the scraper==
The tangential force and the normal force on the scraper due to pressure forces and viscous forces are
:<math>F_t = \frac{2\mu U}{r} \frac{\sin\alpha-\alpha\cos\alpha}{\alpha^2 - \sin^2\alpha}, \quad F_n =\frac{2\mu U}{r} \frac{\alpha\sin\alpha}{\alpha^2 - \sin^2\alpha} </math>
The same scraper force if resolved according to Cartesian coordinates (parallel and perpendicular to the lower plate i.e. <math>F_x = F_t \sin\alpha + F_n \cos\alpha, \ F_y = -F_t \cos\alpha + F_n \sin\alpha</math>) are
:<math>F_x = \frac{2\mu U}{r} \frac{\alpha-\sin\alpha\cos\alpha}{\alpha^2 - \sin^2\alpha}, \quad F_y =\frac{2\mu U}{r} \frac{\sin^2\alpha}{\alpha^2 - \sin^2\alpha} </math>
==References==
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