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The motion of fluid in various canals and pipelines has been sufficiently studied with regard of molecular transport for laminar flows in the framework of the Navier-Stokes equations. When deriving these equations to determine the flow hydrodynamic characteristics, one should assume the shear stress in direct ration to the normal fluid velocity derivative. In order to take into account the group transfers of molecules in the flow, one should take the voltage in direct proportion to the derivative of the liquid acceleration. A joint consideration of the transport mechanisms of individual molecules and their groups in the Navier-Stokes differential equations, form terms with a third derivative. In the framework of this article, using the provisions of operational calculus, an analytical solution is obtained for the stationary motion of an incompressible fluid in a flat pipe, when constant velocity and hydrostatic pressure are set at the inlet. Some numerical results obtained using the developed analytical solutions are presented.

ANALYTICAL SOLUTION OF NAVIER STOKES EQUATION REDUCED TO THE EQUATION OF THIRD ORDER TO STUDY THE MOTION OF LIQUID IN A FLAT PIPE.