Laminar Flow in a Pipe

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Laminar flows in pipes typically occur at Reynolds numbers less than 2000 and are also known as the Hagen-Poiseuille flow.  When flow fully develops, the velocity profile across the channel would be parabolic and the pressure drops linearly along the length of the channel. Analytic solution for laminar flow in such channels can be readily derived. A pipe of radius 0.1 m and length 0.5 m has an average velocity corresponding to a Reynolds of 1000. A parabolic velocity profile corresponding to the analytic expression is specified at the inlet. The correct solution would then be an unchanging velocity distribution in the axial direction with a pressure drop equal to that given by the analytical solution.

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