Geodesic
Exact solutions of the laminar flow of a viscous fluid in straight pipes with non-circular cut
Daghestan Electronic Mathematical Reports, Tome 1 (2014), pp. 84-95

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New exact solutions for the distribution of fluid's velocity in the pipe \linebreak cross section of which is either epitrochoid or epicycloid. With minor changes the solution can be applied to hypotrochoid and hypocycloid cases. A theorem on the exact solution in an open area is proven for an acute angle, and the paradox of a right angle is noted. The approximate solution is proposed for the flow of an equilateral curvilinear lune. The use of the method of variables separation and the obtained new solution for the cross section in the form of circle sector are discussed.
Keywords: laminar flow, conformal mapping, epitrochoid, epicycloid. 
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     author = {Muhtar Guseinovich Alishayev},
     title = {Exact solutions of the laminar flow of a viscous fluid in straight pipes with non-circular cut},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {84--95},
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     year = {2014},
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     url = {http://geodesic.mathdoc.fr/item/DEMR_2014_1_a4/}
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Muhtar Guseinovich Alishayev. Exact solutions of the laminar flow of a viscous fluid in straight pipes with non-circular cut. Daghestan Electronic Mathematical Reports, Tome 1 (2014), pp. 84-95. http://geodesic.mathdoc.fr/item/DEMR_2014_1_a4/