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 Φ_V 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: Gotthilf Heinrich Ludwig Hagen (March 3, 1797 - February 3, 1884) was a German physicist and hydraulic engineer. ... 1797 (MDCCXCVII) was a common year starting on Sunday (see link for calendar) of the Gregorian calendar (or a common year starting on Wednesday of the 11-day-slower Julian calendar). ... 1884 (MDCCCLXXXIV) is a leap year starting on Tuesday (click on link to calendar) of the Gregorian calendar (or a leap year starting on Thursday of the 12-day-slower Julian calendar). ... 1839 was a common year starting on Tuesday (see link for calendar). ... A physical law, scientific law, or a law of nature is a scientific generalization based on empirical observations of physical behavior. ... laminar and turbulent water flow over the hull of a submarine In fluid dynamics, laminar flow is a flow regime characterized by high momentum diffusion, low momentum convection, and pressure and velocity independence from time. ... Stationary can mean: Look up stationary in Wiktionary, the free dictionary. ... In fluid dynamics, potential flow, also known as irrotational flow (of incompressible fluids) is steady flow defined by the equations Note that ∇ · v is something different than ∇ v The equations above imply , or Laplaces equation, holds. ... The pitch drop experiment at the University of Queensland. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ... | Jöns Jakob Berzelius, discoverer of protein 1838 was a common year starting on Monday (see link for calendar). ... 1840 is a leap year starting on Wednesday (link will take you to calendar). ... 1846 was a common year starting on Thursday (see link for calendar). ... Jean Louis Marie Poiseuille pwäz-wÄ“ (April 22, 1799 - December 26, 1869) was a French physician and physiologist. ... 1797 (MDCCXCVII) was a common year starting on Sunday (see link for calendar) of the Gregorian calendar (or a common year starting on Wednesday of the 11-day-slower Julian calendar). ... 1869 (MDCCCLXIX) is a common year starting on Friday (link will take you to calendar) of the Gregorian calendar or a common year starting on Sunday of the 12-day-slower Julian calendar. ...

where V is a volume of the liquid, poured in the time unit t, v_s 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: The velocity of an object is simply its speed in a particular direction. ... The 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. ... The Darcy-Weisbach equation is an important and widely used equation in hydraulics. ... Table of Hydraulics and Hydrostatics, from the 1728 Cyclopaedia. ...

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. The Reynolds number is the ratio of inertial forces (vsρ) to viscous forces (μ/L) and is used for determining whether a flow will be laminar or turbulent. ... The Darcy friction factor is a dimensionless number used in internal flow calculations. ... 1856 was a leap year starting on Tuesday (see link for calendar). ... 1858 (MDCCCLVIII) is a common year starting on Friday of the Gregorian calendar (or a common year starting on Sunday of the 12-day-slower Julian calendar). ... 1859 (MDCCCLIX) is a common year starting on Saturday of the Gregorian calendar (or a common year starting on Monday of the Julian calendar). ... 1860 is the leap year starting on Sunday. ...

The law is also very important specially in hemorheology and hemodynamics, both fields of physiology. Categories: Pages needing attention | Stub ... Categories: Pages needing attention | Stub ... Physiology (in Greek physis = nature and logos = word) is the study of the mechanical, physical, and biochemical functions of living organisms. ...

The Poiseuilles' law was later in 1891 extended to turbulent flow by L. R. Wilberforce, based on Hagenbach's work. 1891 (MDCCCXCI) was a common year starting on Thursday (see link for calendar). ... Turbulent flow around an obstacle; the flow further away is laminar Laminar and turbulent water flow over the hull of a submarine Turbulence creating a vortex on an airplane wing In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by low-momentum diffusion, high momentum convection, and...

Curiosity

The law itself shows what an interesting field this is, as the Darcy-Weisbach equation was studied by a number of other scientists, including Chézy, Weisbach, Darcy, Poiseuille, Hagen, Reynolds, Fanning, Prandtl, Blasius, von Kármán, Nikuradse, Colebrook, White, Rouse, and Moody.

Also note in the formula how strongly the flow depends on the radius. If all else is held constant, a doubling of the radius of the channel results in a sixteen-fold increase in the flow.

electrical circuits analogy

Electricity was originally understood to be a kind of fluid. This hydraulic analogy is still conceptually useful. An electrical network or electrical circuit is an interconnection of analog electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. ... Since electric current is invisible and the processes at play in electronics are often difficult to understand in an intuitive way, it is common to teach electronics using analogies to more common sense objects and processes. ...

Poiseuille's law corresponds to Ohm's law for electrical circuits (V=IR), where the pressure drop Δp^* is analogous to the voltage V and voluminal flow rate Φ_V is analogous to the current I. The term is then seen to be analogous to the electrical resistance R. A voltage source, V, drives an electric current, I , through resistor, R, the three quantities obeying Ohms law: V = IR Ohms law, named after its discoverer Georg Ohm [1], states that the potential difference between two points along a connected path and the current flowing through it are... International danger high voltage symbol. ... In electricity, current refers to electric current, which is the flow of electric charge. ... Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ...

References

• Sutera, Salvatore P., "The history of Poiseuille's law," Annual Review of Fluid Mechanics, Vol. 25, 1993, pp. 1-19