Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time.
Pierre Maurice Marie Duhem (French: [pjɛʁ mɔʁis maʁi dy.ɛm, moʁ-] ; 9 June 1861 – 14 September 1916) was a French theoretical physicist who made significant contributions to thermodynamics, hydrodynamics, and the theory of elasticity. Duhem was also a prolific historian of science, noted especially for his pioneering work on the European Middle Ages. As a philosopher of science, Duhem is credited with the "Duhem–Quine thesis" on the indeterminacy of experimental criteria. Duhem's opposition to positivism was partly informed by his traditionalist Catholicism, an outlook that put him at odds with the dominant academic currents in France during his lifetime.
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of a complex variable of complex numbers. It is helpful in many branches of mathematics, including real analysis, algebraic geometry, number theory, analytic combinatorics, and applied mathematics, as well as in physics, including the branches of hydrodynamics, thermodynamics, quantum mechanics, and twistor theory. By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering.
At first glance, complex analysis is the study of holomorphic functions that are the differentiable functions of a complex variable. By contrast with the real case, a holomorphic functions is always infinitely differentiable and equal to the sum of its Taylor series in some neighborhood of each point of its domain.This makes methods and results of complex analysis significantly different from that of real analysis. In particular, contrarily, with the real case, the domain of every holomorphic function can be uniquely extended to almost the whole complex plane. This implies that the study of real analytic functions needs often the power of complex analysis. This is, in particular, the case in analytic combinatorics.
A wing is a type of fin that produces both lift and drag while moving through air. Wings are defined by two shape characteristics, an airfoil section and a planform. Wing efficiency is expressed as lift-to-drag ratio, which compares the benefit of lift with the air resistance of a given wing shape, as it flies. Aerodynamics includes the study of wing performance in air.
Equivalent foils that move through water are found on hydrofoil power vessels and foiling sailboats that lift out of the water at speed and on submarines that use diving planes to point the boat upwards or downwards, while running submerged. The study of foil performance in water is a subfield of Hydrodynamics.
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of a complex variable of complex numbers. It is helpful in many branches of mathematics, including real analysis, algebraic geometry, number theory, analytic combinatorics, and applied mathematics, as well as in physics, including the branches of hydrodynamics, thermodynamics, quantum mechanics, and twistor theory. By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering.
At first glance, complex analysis is the study of holomorphic functions that are the differentiable functions of a complex variable. By contrast with the real case, a holomorphic function is always infinitely differentiable and equal to the sum of its Taylor series in some neighborhood of each point of its domain.This makes methods and results of complex analysis significantly different from that of real analysis. In particular, contrarily, with the real case, the domain of every holomorphic function can be uniquely extended to almost the whole complex plane. This implies that the study of real analytic functions needs often the power of complex analysis. This is, in particular, the case in analytic combinatorics.
Johann Peter Gustav Lejeune Dirichlet (/ˌdɪərɪˈkleɪ/; German: [ləˈʒœn diʁiˈkleː]; 13 February 1805 – 5 May 1859) was a German mathematician. In number theory, he proved special cases of Fermat's Last Theorem and created analytic number theory. In analysis, he advanced the theory of Fourier series and was one of the first to give the modern formal definition of a function. In mathematical physics, he studied potential theory, boundary-value problems, heat diffusion, and hydrodynamics.
Although his surname is Lejeune Dirichlet, he is commonly referred to by his mononym Dirichlet, in particular for results named after him.
In hydrodynamics, a plume or a column is a vertical body of one fluid moving through another. Several effects control the motion of the fluid, including momentum (inertia), diffusion (temperature, viscosity, surface tension), and buoyancy (differences in mass density). Jets and plumes deemed "pure" represent flows that are driven entirely by momentum and buoyancy, respectively. Flows occurring between these limiting cases are usually characterized as buoyant jets and forced plumes.
A plume is said to be positively buoyant when, in the absence of additional external forces or initial conditions, the column of fluid tends to rise. By contrast, a plume is said to be negatively buoyant when the density of the column is greater than its surroundings (statically, its natural tendency would be to sink), but the flow has sufficient initial momentum to exhibit a rise.
In fluid dynamics, the drag coefficient (commonly denoted as: , or ) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the drag equation in which a lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag. The drag coefficient is always associated with a particular surface area.
The drag coefficient of any object comprises the effects of the two basic contributors to fluid dynamic drag: skin friction and form drag. The drag coefficient of a lifting airfoil or hydrofoil also includes the effects of lift-induced drag. The drag coefficient of a complete structure such as an aircraft also includes the effects of interference drag.
