Poiseuille's law

The Poiseuille's law (or the Hagen-Poiseuille law also named after Gotthilf Heinrich Ludwig Hagen (1797-1884) for his experiments in 1839) is the physical law concerning the voluminal laminar stationary flow ΦV of incompressible uniform viscous liquid (so called Newtonian fluid) through a cylindrical tube with the constant circular cross-section, experimentally derived in 1838, formulated and published in 1840 and 1846 by Jean Louis Marie Poiseuille (1797-1869), and defined by:

Related Topics:
Gotthilf Heinrich Ludwig Hagen - 1797 - 1884 - 1839 - Physical law - Laminar - Stationary - Incompressible - Viscous - Newtonian fluid - 1838 - 1840 - 1846 - Jean Louis Marie Poiseuille - 1869

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: Phi_{V} = {dVover dt} = v_{s}pi r^{2} = {pi r^{4}over 8 eta} left( - { d p^{star} over dz} ight) = {pi r^{4}over 8 eta} { Delta p^{star} over ell} ; ,

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where V is a volume of the liquid, poured in the time unit t, vs median fluid velocity along the axial cylindrical coordinate z, r internal radius of the tube, Δp* the pressure drop at the two ends, η dynamic fluid viscosity and l characteristic length along z, a linear dimension in a cross-section (in non-cylindrical tube). The law can be derived from the Darcy-Weisbach equation, developed in the field of hydraulics and which is otherwise valid for all types of flow, and also expressed in the form:

Related Topics:
Velocity - Cylindrical coordinate - Darcy-Weisbach equation - Hydraulics

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: Lambda = {64over {it Re}} ; , quadquad Re = {2 ho v_{s} rover eta} ; ,

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where Re is the Reynolds number and ρ fluid density. In this form the law approximates the Darcy friction factor, the energy (head) loss factor, friction loss factor or Darcy (friction) factor Λ in the laminar flow at very low velocities in cylindrical tube. The theoretical derivation of slightly different Poiseuille's original form of the law was made independently by Wiedman in 1856 and Neumann and E. Hagenbach in 1858 (1859, 1860). Hagenbach was the first who called this law the Poiseuille's law.

Related Topics:
Reynolds number - Darcy friction factor - 1856 - 1858 - 1859 - 1860

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The law is also very important specially in hemorheology and hemodynamics, both fields of physiology.

Related Topics:
Hemorheology - Hemodynamics - Physiology

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The Poiseuilles' law was later in 1891 extended to turbulent flow by L. R. Wilberforce, based on Hagenbach's work.

Related Topics:
1891 - Turbulent flow

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