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 , or the flow through a drinking straw or through a hypodermic needle. 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. Poiseuille's Equation describes the pressure drop due to the viscosity of the fluid; Other types of pressure drops may still occur in a fluid see a demonstration here . For example, the pressure needed to drive a viscous fluid up against gravity would contain both that as needed in Poiseuille's Law plus that as needed in Bernoulli's equation , such that any point in the flow would have a pressure greater than zero otherwise no flow would happen.
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