### Math modeling

### Daghestan Electronic Mathematical Reports: Issue 1 (2014)

# Exact solutions of the laminar flow of a viscous fluid in straight pipes with non-circular cut

### UDK: 519.6+532.5

### Pages: 84 - 95

### DOI: 10.31029/demr.1.5

New exact solutions for the distribution of fluid's velocity in the pipe 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.