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where V is a volume of the liquid, poured in the time unit t, vs median fluid velocityVelocity (symbol: v is a vector measurement of the rate and direction of motion. The scalar absolute value ( magnitude) of velocity is speed. Velocity can also be defined as rate of change of displacement or just as the rate of displacement, depending on along the axial cylindrical coordinateThe cylindrical coordinate system is a three-dimensional system which essentially extends circular polar coordinates by adding a third coordinate (usually denoted ) which measures the height of a point above the plane. A point P is given as. In terms of t z, r internal radius of the tube, Δp* the preasure 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 equationFluid dynamics The Darcy-Weisbach equation is an important and widely used equation in hydraulics. It enables calculation of the head loss due to friction within a given run of pipe. The equation was initially a variant on the Prony equation; this variant, developed in the field of hydraulicsHydraulics is a branch of science and engineering concerned with the use of liquids to perform mechanical tasks. It is part of the more general discipline of fluid power. The word "hydraulics" comes from the Greek word hydraulikos which in turn comes from and which is otherwise valid for all types of flow, and also expressed in the form:
where Re is the Reynolds numberThe Reynolds number is the most important dimensionless number in fluid dynamics and provides a criterion for dynamic similarity; in other words when two similar objects of possibly different sizes in perhaps different fluids with different flowrates will and ρ fluid density. In this form the law approximates the friction factorThe Darcy friction factor is a dimensionless number used in internal flow calculations. It expresses the linear relationship between mean flow velocity and pressure gradient. It is defined as: where: is the pressure drop per unit length is the hydraulic d, 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 1856Events January 8 Borax is discovered ( John Veatch). January 29 Queen Victoria institutes the Victoria Cross February 18 The American Party ( Know-Nothings) convene in Philadelphia, Pennsylvania to nominate their first Presidential candidate, former Presi and Neumann and E. Hagenbach in 1858Events January 14 Felice Orsini and his accomplices fail to assassinate Napoleon III in Paris but their bombs kill 156 bystanders. Because of the involvement of French emigres living in Britain, there is a brief anti-British feeling in France but the empe ( 1859, 1860). Hagenbach was the first who called this law the Poiseuille's law.
The law is also very important specially in hemorheology and hemodynamics, both fields of physiology.
The Poiseuilles' law was later in 1891 extended to turbulent flow by L. R. Wilberforce, based on Hagenbach's work.