Engineering Physics Annotation << Back TO THE QUESTION ON THE FLOW OF LIQUIDS IN PIPES AND CHANNELS OF ARBITRARYCROSS-SECTION S.O. GLADKOV, ZAW AUNG An analytical description of the hydrodynamic flow of fluid through a pipe of arbitrary cross-section under the action of a constant pressure gradient is proposed. Proceeding from the general principles of hydrodynamics of viscous liquids, the distribution of velocity and section of the pipe is found. As examples, several special cases are considered. A general algorithm for solving such problems is given and as illustrative examples, the flow of fluid through a channel is considered, the crosssection of which is a piecewise smooth contour, in particular, an arbitrary triangle and a rectangle. A general formula for the functional dependence and velocity of flow vz from coordinates x, y in the case of an arbitrary shape of the contour is given, provided that the axis is directed along the axis z of the channel. Due to this formula provides a general expression to calculate the flow rate of fluid flowing per unit time through a channel of any cross-section. Keywords: dynamic viscosity, pressure gradient, Navier-Stokes equation, continuity equation, pipe cross-section, piecewise smooth contour, random section channel. DOI: 10.25791/infizik.10.2021.1230 Pp. 27-36.