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Chézy Formula
The Chézy formula is an semi-empirical resistance equation which estimates mean flow velocity in Open-channel flow, open channel conduits. The relationship was realized and developed in 1768 by French physicist and engineer Antoine de Chézy (1718–1798) while designing Paris's water canal system. Chézy discovered a similarity parameter that could be used for estimating flow characteristics in one channel based on the measurements of another. The Chézy formula relates the flow of water through an open channel with the channel's dimensions and slope. The Chézy equation is a pioneering formula in the field of fluid mechanics and was expanded and modified by Irish Engineer Robert Manning (engineer), Robert Manning in 1889.Manning, R., "On the flow of Water in Open Channels and Pipes." ''Transactions Institute of Civil Engineers of Ireland, vol. 20, pp. 161–209, Dublin, 1891, Supplement, vol 24, pp. 179–207, 1895'' Manning's modifications to the Chézy formula allowed the entire ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flow Velocity
In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the flow velocity vector is the flow speed and is a scalar. It is also called velocity field; when evaluated along a line, it is called a velocity profile (as in, e.g., law of the wall). Definition The flow velocity ''u'' of a fluid is a vector field : \mathbf=\mathbf(\mathbf,t), which gives the velocity of an '' element of fluid'' at a position \mathbf\, and time t.\, The flow speed ''q'' is the length of the flow velocity vector :q = \, \mathbf \, and is a scalar field. Uses The flow velocity of a fluid effectively describes everything about the motion of a fluid. Many physical properties of a fluid can be expressed mathematically in terms of the flow velocity. Some common examples follow: Steady flow The flow of a fluid is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Navier–Stokes Equations
In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842–1850 (Stokes). The Navier–Stokes equations mathematically express conservation of momentum and conservation of mass for Newtonian fluids. They are sometimes accompanied by an equation of state relating pressure, temperature and density. They arise from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing ''viscous flow''. The difference between them and the closely related Euler equations is that Navier–Stokes equations take ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sir George Stokes, 1st Baronet
Sir George Gabriel Stokes, 1st Baronet, (; 13 August 1819 – 1 February 1903) was an Irish English physicist and mathematician. Born in County Sligo, Ireland, Stokes spent all of his career at the University of Cambridge, where he was the Lucasian Professor of Mathematics from 1849 until his death in 1903. As a physicist, Stokes made seminal contributions to fluid mechanics, including the Navier–Stokes equations; and to physical optics, with notable works on polarization and fluorescence. As a mathematician, he popularised "Stokes' theorem" in vector calculus and contributed to the theory of asymptotic expansions. Stokes, along with Felix Hoppe-Seyler, first demonstrated the oxygen transport function of hemoglobin and showed color changes produced by aeration of hemoglobin solutions. Stokes was made a baronet by the British monarch in 1889. In 1893 he received the Royal Society's Copley Medal, then the most prestigious scientific prize in the world, "for his researches and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Julius Ludwig Weisbach
Julius Ludwig Weisbach (born 10 August 1806 in Mittelschmiedeberg (now Mildenau Municipality), Erzgebirge, died 24 February 1871, Freiberg) was a German mathematician and engineer. Life and work Weisbach studied at the '' Bergakademie'' in Freiberg from 1822 - 1826. After that, he studied with Carl Friedrich Gauss in Göttingen and with Friedrich Mohs in Vienna. In 1831 he returned to Freiberg where he worked as mathematics teacher at the local Gymnasium. In 1833 he became teacher for Mathematics and the Theory of Mountain Machines at the Freiberg ''Bergakademie''. In 1836 he was promoted to Professor for applied mathematics, mechanics, theory of mountain machines and so-called ''Markscheidekunst''. Weisbach wrote an influential book for mechanical engineering students, called ''Lehrbuch der Ingenieur- und Maschinenmechanik'', which has been expanded and reprinted on numerous occasions between 1845 and 1863. He also refined the Darcy equation into the still widely used Da ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henry Darcy
Henry Philibert Gaspard Darcy (, 10 June 1803 – 3 January 1858) was a French engineer who made several important contributions to hydraulics, including Darcy’s law for flow in porous media. Early life Darcy was born in Dijon, France, on June 10, 1803. His first given name is ''Henry''; although the French spelling ''Henri'' appears in multiple sources such as necrological notices, Darcy used the Anglicized spelling. Despite his father's death in 1817 when he was 14, his mother was able to borrow money to pay for his tutors. In 1821 he enrolled at the ''École Polytechnique'' (Polytechnic School) in Paris, and transferred two years later to the School of Bridges and Roads, which led to employment in the Corps of Bridges and Roads. Darcy met an English woman, Henriette Carey, whose family had been living in Dijon, and married her in 1828. Engineering career As a member of the Corps, he built an adequate pressurized water distribution system in Dijon following the failur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean Léonard Marie Poiseuille
Jean Léonard Marie Poiseuille (; 22 April 1797 – 26 December 1869) was a French physicist and physiologist. Poiseuille was born in Paris, France, and he died there on 26 December 1869. Fluid flow From 1815 to 1816 he studied at the École Polytechnique in Paris. He was trained in physics and mathematics. In 1828 he earned his D.Sc. degree with a dissertation entitled ''Recherches sur la force du coeur aortique''. He was interested in the flow of human blood in narrow tubes. In 1838 he experimentally derived, and in 1840 and 1846 formulated and published, Poiseuille's law (now commonly known as the Hagen–Poiseuille equation, crediting Gotthilf Hagen as well), which applies to laminar flow, that is, non-turbulent flow of liquids through pipes of uniform section, such as blood flow in capillaries and veins. His original formulation for water of 1846 little resembles the present-day formulation and is given as: : \dot = \left(135.282 \mathrm \right) \frac \left(1+\frac\,T + ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gotthilf Hagen
Gotthilf Heinrich Ludwig Hagen (3 March 1797 – 3 February 1884) was a German civil engineer who made important contributions to fluid dynamics, hydraulic engineering and probability theory. Life and work Hagen was born in Königsberg, East Prussia (Kaliningrad, Russia) to Friedrich Ludwig Hagen and Helene Charlotte Albertine Hagen.Schroeder, Ralph, "Hagen, Gotthilf Heinrich Ludwig" in: New German Biography 7 (1966), p 472 nline version URL: http://www.deutsche-biographie.de/ppn118719874.html His father was a government official and his mother was the daughter of Christian Reccard, professor of Theology at University of Königsberg, consistorial councillor and astronomer. He showed promise in mathematics in high school and he went on to study at the University of Königsberg where his uncle, Karl Gottfried Hagen was professor of physics and chemistry. In 1816 Hagen began studying mathematics and astronomy with Friedrich Wilhelm Bessel, but in 1818 he switched to study civil en ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adhémar Jean Claude Barré De Saint-Venant
Adhémar Jean Claude Barré de Saint-Venant (23 August 1797 – 6 January 1886) was a mechanician and mathematician who contributed to early stress analysis and also developed the unsteady open channel flow shallow water equations, also known as the Saint-Venant equations that are a fundamental set of equations used in modern hydraulic engineering. The one-dimensional Saint-Venant equation is a commonly used simplification of the shallow water equations. Although his full surname was Barré de Saint-Venant in mathematical literature other than French he is known as Saint-Venant. His name is also associated with Saint-Venant's principle of statically equivalent systems of load, Saint-Venant's theorem and for Saint-Venant's compatibility condition, the integrability conditions for a symmetric tensor field to be a strain. In 1843 he published the correct derivation of the Navier–Stokes equations for a viscous flow and was the first to "properly identify the coefficient of viscosit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Claude-Louis Navier
Claude-Louis Navier (born Claude Louis Marie Henri Navier; ; 10 February 1785 – 21 August 1836) was a French mechanical engineer, affiliated with the French government, and a physicist who specialized in continuum mechanics. The Navier–Stokes equations refer eponymously to him, with George Gabriel Stokes. Biography After the death of his father in 1793, Navier's mother left his education in the hands of his uncle Émiland Gauthey, an engineer with the Corps of Bridges and Roads ''(Corps des Ponts et Chaussées)''. In 1802, Navier enrolled at the École polytechnique, and in 1804 continued his studies at the École Nationale des Ponts et Chaussées, from which he graduated in 1806. He eventually succeeded his uncle as ''Inspecteur general'' at the Corps des Ponts et Chaussées. He directed the construction of bridges at Choisy, Asnières and Argenteuil in the Department of the Seine, and built a footbridge to the Île de la Cité in Paris. His 1824 design for the Pont ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Albert Brahms
Albert Brahms (October 24, 1692 – August 3, 1758) was a Frisian dike judge, an elected community leader responsible for maintaining the dikes that protected the area against the Wadden Sea, and a pioneer of hydraulic engineering. Biography Brahms was born on October 24, 1692, in Sanderahm, Sande, in what is now the Friesland district of Lower Saxony, Germany.. He was elected as dike judge in 1718, after the disastrous Christmas flood of 1717, which had caused many deaths, and he retained the position until 1752., p. 12. For his work in dike engineering, he was honored as a "princely geometer" of the Principality of Anhalt-Zerbst Anhalt-Zerbst was a principality of the Holy Roman Empire ruled by the House of Ascania, with its residence at Zerbst in present-day Saxony-Anhalt. It emerged as a subdivision of the Principality of Anhalt from 1252 until 1396, when it was divided ... (german: "hochfürstlich Anhalt-Zerbstischer Geometer"), to which Sande at that time belonged. Coa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hazen–Williams Equation
The Hazen–Williams equation is an empirical relationship which relates the flow of water in a pipe with the physical properties of the pipe and the pressure drop caused by friction. It is used in the design of water pipe systems such as fire sprinkler systems, water supply networks, and irrigation systems. It is named after Allen Hazen and Gardner Stewart Williams. The Hazen–Williams equation has the advantage that the coefficient ''C'' is not a function of the Reynolds number, but it has the disadvantage that it is only valid for water. Also, it does not account for the temperature or viscosity of the water, and therefore is only valid at room temperature and conventional velocities. General form Henri Pitot discovered that the velocity of a fluid was proportional to the square root of its head in the early 18th century. It takes energy to push a fluid through a pipe, and Antoine de Chézy discovered that the hydraulic head loss was proportional to the velocity squared. Conse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Darcy–Weisbach Equation
In fluid dynamics, the Darcy–Weisbach equation is an empirical equation that relates the head loss, or pressure loss, due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressible fluid. The equation is named after Henry Darcy and Julius Weisbach. Currently, there is no formula more accurate or universally applicable than the Darcy-Weisbach supplemented by the Moody diagram or Colebrook equation. The Darcy–Weisbach equation contains a dimensionless friction factor, known as the Darcy friction factor. This is also variously called the Darcy–Weisbach friction factor, friction factor, resistance coefficient, or flow coefficient. Pressure-loss equation In a cylindrical pipe of uniform diameter , flowing full, the pressure loss due to viscous effects is proportional to length and can be characterized by the Darcy–Weisbach equation: :\frac =f_\mathrm \cdot \frac \cdot \frac, where the pressure loss per unit length (SI units: P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
