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The Hagen–Poiseuille equation can be derived from the Navier–Stokes equations. The laminar flow through a pipe of uniform (circular) cross-section is known as Hagen–Poiseuille flow. The equations governing the Hagen–Poiseuille flow can be derived directly from the Navier–Stokes momentum equations in 3D cylindrical coordinates ( r , θ ...
In fluid dynamics, the Hagen–Poiseuille equation is a physical law that gives the pressure drop in a fluid flowing through a long cylindrical pipe. The assumptions of the equation are that the flow is laminar viscous and incompressible and the flow is through a constant circular cross-section that is substantially longer than its diameter.
In Hagen–Poiseuille equation, the flow layers start from the wall and, by viscosity, reach each other in the central line of the vessel following a parabolic velocity profile. [ citation needed ] In a second approach, more realistic and coming from experimental observations on blood flows, according to Thurston, [ 7 ] there is a plasma ...
In 1838 he experimentally derived, and in 1840 and 1846 formulated and published, Poiseuille's law (now commonly known as the Hagen–Poiseuille equation, crediting Gotthilf Hagen as well), which applies to laminar flow, that is, non-turbulent flow of liquids through pipes of uniform section, such as blood flow in capillaries and veins.
Friction loss under conditions of laminar flow follow the Hagen–Poiseuille equation, which is an exact solution to the Navier-Stokes equations. For a circular pipe with a fluid of density ρ and viscosity μ , the hydraulic slope S can be expressed
Hagen–Poiseuille equation Gotthilf Heinrich Ludwig Hagen (3 March 1797 – 3 February 1884) was a German civil engineer who made important contributions to fluid dynamics , hydraulic engineering and probability theory.
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The poiseuille (symbol Pl) has been proposed as a derived SI unit of dynamic viscosity, [1] named after the French physicist Jean Léonard Marie Poiseuille (1797–1869).. In practice the unit has never been widely accepted and most international standards bodies do not include the poiseuille in their list of units.