<Tr> <Td> <Ul> <Li> </Li> <Li> </Li> <Li> </Li> </Ul> </Td> </Tr> <Ul> <Li> </Li> <Li> </Li> <Li> </Li> </Ul> <P> In nonideal fluid dynamics, the Hagen--Poiseuille equation, also known as the Hagen--Poiseuille law, Poiseuille law or Poiseuille equation, is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross section . It can be successfully applied to air flow in lung alveoli, for the flow through a drinking straw or through a hypodermic needle . It was experimentally derived independently by Jean Léonard Marie Poiseuille in 1838 and Gotthilf Heinrich Ludwig Hagen, and published by Poiseuille in 1840--41 and 1846 . </P> <P> The assumptions of the equation are that the fluid is incompressible and Newtonian; the flow is laminar through a pipe of constant circular cross-section that is substantially longer than its diameter; and there is no acceleration of fluid in the pipe . For velocities and pipe diameters above a threshold, actual fluid flow is not laminar but turbulent, leading to larger pressure drops than calculated by the Hagen--Poiseuille equation . </P>

The velocity distribution in laminar flow through a circular pipe follows the law