The scientific principle which explains that in fluid flow an increase in velocity is associated with a decrease in pressure is named after which family of mathematicians and physicists?
"of a steady irrotational flow, in which case and are constants so equation () can be applied in every point of the fluid domain. Further can be made equal to zero by incorporating it into the velocity potential using the transformation resulting in Note that the relation of the potential to the flow velocity is unaffected by this transformation: . The Bernoulli equation for unsteady potential flow also appears to play a central role in Luke's variational principle, a variational description of free-surface flows using the Lagrangian (not to be confused with Lagrangian coordinates). Bernoulli developed his principle from his"
"Venturi effect The Venturi effect is the reduction in fluid pressure that results when a fluid flows through a constricted section (or choke) of a pipe. The Venturi effect is named after Giovanni Battista Venturi (1746–1822), an Italian physicist. In fluid dynamics, an incompressible fluid's velocity must ""increase"" as it passes through a constriction in accord with the principle of mass continuity, while its static pressure must ""decrease"" in accord with the principle of conservation of mechanical energy. Thus any gain in kinetic energy a fluid may accrue due to its increased velocity through a constriction is balanced by a"
"Crocco's theorem Crocco's theorem is an aerodynamic theorem relating the flow velocity, vorticity, and stagnation pressure (or entropy) of a potential flow. Crocco's theorem gives the relation between the thermodynamics and fluid kinematics. The theorem was first enunciated by Alexander Friedmann for the particular case of a perfect gas and published in 1922: However, usually this theorem is connected with the name of Italian scientist Luigi Crocco, a son of Gaetano Crocco. Consider an element of fluid in the flow field subjected to translational and rotational motion: because stagnation pressure loss and entropy generation can be viewed as essentially the"
"Leonardo da Vinci (1452–1519) performed experiments, investigated and speculated on waves and jets, eddies and streamlining. Isaac Newton (1642–1727) by formulating the laws of motion and his law of viscosity, in addition to developing the calculus, paved the way for many great developments in fluid mechanics. Using Newton's laws of motion, numerous 18th-century mathematicians solved many frictionless (zero-viscosity) flow problems. However, most flows are dominated by viscous effects, so engineers of the 17th and 18th centuries found the inviscid flow solutions unsuitable, and by experimentation they developed empirical equations, thus establishing the science of hydraulics. Late in the 19th century,"
"Pascal's law Pascal's law (also Pascal's principle or the principle of transmission of fluid-pressure) is a principle in fluid mechanics that states that pressure at a point, has infinite direction, and thus a pressure change at any point in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere. The law was established by French mathematician Blaise Pascal in 1647–48. Pascal's principle is defined as This principle is stated mathematically as: The intuitive explanation of this formula is that the change in pressure between two elevations is due to the weight of the fluid"
"Navier–Stokes equations In physics, the Navier–Stokes equations (), named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous fluid substances. These balance equations 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 main difference between them and the simpler Euler equations for inviscid flow is that Navier–Stokes equations also factor in the Froude limit (no external field) and are not conservation equations, but rather"
"Prandtl–Batchelor theorem In fluid dynamics, Prandtl–Batchelor theorem states that ""if in a two-dimensional laminar flow at high Reynolds number closed streamlines occur, then the vorticity in the closed streamline region must be a constant"". The theorem is named after Ludwig Prandtl and George Batchelor. Prandtl in his celebrated 1904 paper stated this theorem in arguments, George Batchelor unaware of this work proved the theorem in 1956. Interestingly, the problem was also studied in the same year by Richard Feynman and Paco Lagerstrom and by W.W. Wood in 1957. At high Reynolds numbers, Euler equations reduce to solving a problem for"
"Taylor–Proudman theorem In fluid mechanics, the Taylor–Proudman theorem (after Geoffrey Ingram Taylor and Joseph Proudman) states that when a solid body is moved slowly within a fluid that is steadily rotated with a high angular velocity formula_1, the fluid velocity will be uniform along any line parallel to the axis of rotation. formula_1 must be large compared to the movement of the solid body in order to make the Coriolis force large compared to the acceleration terms. The Navier–Stokes equations for steady flow, with zero viscosity and a body force corresponding to the Coriolis force, are where formula_4 is the"
"flows through the Venturi the pressure in the two ends of the tube will differ, forcing the liquid to the ""low pressure"" side. The amount of that move can be calibrated to the speed of the fluid flow. Venturi effect The Venturi effect is the reduction in fluid pressure that results when a fluid flows through a constricted section (or choke) of a pipe. The Venturi effect is named after Giovanni Battista Venturi (1746–1822), an Italian physicist. In fluid dynamics, an incompressible fluid's velocity must ""increase"" as it passes through a constriction in accord with the principle of mass continuity,"
"credited with the discovery of Archimedes' Principle, which relates the buoyancy force on an object that is submerged in a fluid to the weight of fluid displaced by the object. The Roman engineer Vitruvius warned readers about lead pipes bursting under hydrostatic pressure. The concept of pressure and the way it is transmitted by fluids was formulated by the French mathematician and philosopher Blaise Pascal in 1647. The ""fair cup"" or Pythagorean cup, which dates from about the 6th century BC, is a hydraulic technology whose invention is credited to the Greek mathematician and geometer Pythagoras. It was used as"
"BC, was the first person to formally assert that a fluid could be treated as a continuum. Archimedes also introduced the concept that fluid flow was driven by a pressure gradient within the fluid. This idea would later prove fundamental to the understanding of fluid flow. In 1687, Newton's ""Principia"" presented Newton's laws of motion, the first complete theoretical approach to understanding mechanical phenomena. In particular, Newton's second law, a statement of the conservation of momentum, is one of three fundamental physical principles used to obtain the Euler equations and Navier-Stokes equations. In 1738, the Dutch-Swiss mathematician Daniel Bernoulli published"
"reversibility. This type of flow is named in honor of Maurice Couette, a Professor of Physics at the French University of Angers in the late 19th century. Couette flow is frequently used in undergraduate physics and engineering courses to illustrate shear-driven fluid motion. The simplest conceptual configuration finds two infinite, parallel plates separated by a distance formula_1. One plate, say the top one, translates with a constant velocity formula_2 in its own plane. Neglecting pressure gradients, the Navier–Stokes equations simplify to where formula_4 is a spatial coordinate normal to the plates and formula_5 is the velocity distribution. This equation reflects"
"(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. The equation in standard fluid dynamics notation is or or formula_3 where: The poise, the unit of viscosity in the CGS system, was named after him. Attempts to introduce ""poiseuille"" as the name of the SI unit Pa·s had little success. Jean Léonard Marie Poiseuille Jean Léonard Marie Poiseuille (; 22 April 1797 – 26 December 1869) was a French physicist and physiologist. Poiseuille"
"for pressure. Mathematically this law is now written: where P is pressure, ρ is the density of the fluid and u is its velocity. In his 1738 book ""Specimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk)"", Bernoulli offered a solution to the St. Petersburg paradox as the basis of the economic theory of risk aversion, risk premium, and utility. Bernoulli often noticed that when making decisions that involved some uncertainty, people did not always try to maximize their possible monetary gain, but rather tried to maximize ""utility"", an economic term encompassing their"
"Basset–Boussinesq–Oseen equation In fluid dynamics, the Basset–Boussinesq–Oseen equation (BBO equation) describes the motion of – and forces on – a small particle in unsteady flow at low Reynolds numbers. The equation is named after Joseph Valentin Boussinesq, Alfred Barnard Basset and Carl Wilhelm Oseen. The BBO equation, in the formulation as given by and , pertains to a small spherical particle of diameter formula_1 having mean density formula_2 whose center is located at formula_3. The particle moves with Lagrangian velocity formula_4 in a fluid of density formula_5, dynamic viscosity formula_6 and Eulerian velocity field formula_7. The fluid velocity field surrounding"
"a theory of gravitation has to explain those laws and must not presuppose them. In a 1675 letter to Henry Oldenburg, and later to Robert Boyle, Newton wrote the following: [Gravity is the result of] “a condensation causing a flow of ether with a corresponding thinning of the ether density associated with the increased velocity of flow.” He also asserted that such a process was consistent with all his other work and Kepler's Laws of Motion. Newtons' idea of a pressure drop associated with increased velocity of flow was mathematically formalised as Bernoulli's principle published in Daniel Bernoulli's book ""Hydrodynamica"""
"sum of pressure and gravitational potential ) is the same everywhere. Bernoulli's principle can also be derived directly from Isaac Newton's Second Law of Motion. If a small volume of fluid is flowing horizontally from a region of high pressure to a region of low pressure, then there is more pressure behind than in front. This gives a net force on the volume, accelerating it along the streamline. Fluid particles are subject only to pressure and their own weight. If a fluid is flowing horizontally and along a section of a streamline, where the speed increases it can only be"
"to the assumptions. Obviously this disobeys our observations. Our observations show that the greater the velocity (or momentum), the more fluid fraction through the straight direction. Only under very slow laminar flow, Q may be equal to Q. The question raised from the experiments by McNown and by Acrivos et al. Their experimental results showed a pressure rise after T-junction due to flow branching. This phenomenon was explained by Wang. Because of inertial effects, the fluid will prefer to the straight direction. Thus the flow rate of the straight pipe is greater than that of the vertical one. Furthermore, because"
"temperature or viscosity of the water. 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. Consequently, the Chézy formula relates hydraulic slope ""S"" (head loss per unit length) to the fluid velocity ""V"" and hydraulic radius ""R"": The variable ""C"" expresses the proportionality, but the value of ""C"" is not a constant. In 1838 and 1839, Gotthilf Hagen and Jean"
"of formula_9 Note that in the Navier–Stokes equations formula_7 is the fluid velocity field, while, as indicated above, in the BBO equation formula_21 is the velocity of the undisturbed flow as seen by an observer moving with the particle. Thus, even in steady Eulerian flow formula_8 depends on time if the Eulerian field is non-uniform. Basset–Boussinesq–Oseen equation In fluid dynamics, the Basset–Boussinesq–Oseen equation (BBO equation) describes the motion of – and forces on – a small particle in unsteady flow at low Reynolds numbers. The equation is named after Joseph Valentin Boussinesq, Alfred Barnard Basset and Carl Wilhelm Oseen. The"
"is, it leaves out the Bernoulli part of the interaction. Explanations based on Increased flow speed and Bernoulli's principle first try to establish that there is higher flow speed over the upper surface, but they fail to explain correctly what causes the flow to speed up: Bernoulli-only explanations imply that a speed difference arises from causes other than a pressure difference, and that the speed difference then leads to a pressure difference by Bernoulli’s principle. This implied one-way causation is a misconception. The real cause-and-effect relationship between pressure and velocity is reciprocal. Finally, Bernoulli-only explanations don't explain how the pressure"
"Faxén's law In fluid dynamics, Faxén's laws relate a sphere's velocity formula_1 and angular velocity formula_2 to the forces, torque, stresslet and flow it experiences under low Reynolds number (creeping flow) conditions. Faxen's first law was introduced in 1922 by Swedish physicist Hilding Faxén, who at the time was active at Uppsala University, and is given by where It can also be written in the form where formula_11 is the mobility. In the case that the pressure gradient is small compared with the length scale of the sphere's diameter, and when there is no external force, the last two terms"
"Jeffery–Hamel flow In fluid dynamics Jeffery–Hamel flow is a flow created by a converging or diverging channel with a source or sink of fluid volume at the point of intersection of the two plane walls. It is named after George Barker Jeffery(1915) and Georg Hamel(1917), but it has subsequently been studied by many major scientists such as von Kármán and Levi-Civita, Walter Tollmien, F. Noether, W.R. Dean, Rosenhead, Landau, G.K. Batchelor etc. Consider two stationary plane walls with a constant volume flow rate formula_1 is injected/sucked at the point of intersection of plane walls and let the angle subtended by"
"to formula_48 implies an formula_49 (small) phase difference between elevation formula_38 and velocity formula_51. For sinusoidal waves with velocity amplitude formula_52 the flow velocities shoal to leading order as This could have been anticipated since for a horizontal bed formula_54 with formula_8 the wave amplitude. Green's law In fluid dynamics, Green's law describes the evolution of non-breaking surface gravity waves propagating in shallow water of gradually varying depth and width. The law is named after George Green. In its simplest form, for wavefronts and depth contours parallel to each other (and the coast), it states: where formula_3 and formula_4 are"
"original direction of the current. But as he was unacquainted with the law of the velocities of running water as depending upon the depth of the orifice, the want of precision which appears in his results is not surprising. Islamicate scientists, particularly Abu Rayhan Biruni (973–1048) and later Al-Khazini (fl. 1115–1130), were the first to apply experimental scientific methods to fluid mechanics, especially in the field of fluid statics, such as for determining specific weights. They applied the mathematical theories of ratios and infinitesimal techniques, and introduced algebraic and fine calculation techniques into the field of fluid statics. In fluid"
"including Isaac Newton, Evangelista Torricelli and Francesco Redi conducted experiments focusing on the flow of water, measuring atmospheric pressure using a barometer and disproving spontaneous generation. Scientific societies and scientific journals emerged and were spread widely through the printing press, touching off the scientific revolution. Newton in 1687 published his ""The Mathematical Principles of Natural Philosophy"", or ""Principia Mathematica"", which set the groundwork for physical laws that remained current until the 19th century. Some modern scholars, including Andrew Cunningham, Perry Williams and Floris Cohen, argue that natural philosophy is not properly called a science, and that genuine scientific inquiry began"
"geometry with transpiration velocities on the walls. Chia-Shun Yih found a solution in 1958 for Poiseuille flow into a sink when formula_64. Beltrami flow In fluid dynamics, Beltrami flows are flows in which the vorticity vector formula_1 and the velocity vector formula_2 are parallel to each other. In other words, Beltrami flow is a flow where Lamb vector is zero. It is named after the Italian mathematician Eugenio Beltrami due to his derivation of the Beltrami vector field, while initial developments in fluid dynamics were done by the Russian scientist Ippolit S. Gromeka in 1881. Since the vorticity vector formula_3"
"by Brook Taylor and by Jean le Rond d'Alembert. Together Bernoulli and Euler tried to discover more about the flow of fluids. In particular, they wanted to know about the relationship between the speed at which blood flows and its pressure. To investigate this, Daniel experimented by puncturing the wall of a pipe with a small open ended straw and noted that the height to which the fluid rose up the straw was related to fluid's pressure in the pipe. Soon physicians all over Europe were measuring patients' blood pressure by sticking point-ended glass tubes directly into their arteries. It"
"of the gas, and ""k"" is a constant. The equation states that the product of pressure and volume is a constant for a given mass of confined gas and this holds as long as the temperature is constant. For comparing the same substance under two different sets of conditions, the law can be usefully expressed as The equation shows that, as volume increases, the pressure of the gas decreases in proportion. Similarly, as volume decreases, the pressure of the gas increases. The law was named after chemist and physicist Robert Boyle, who published the original law in 1662. This relationship"
"volume changes with temperature. Thus this law is sometimes referred to as Mariotte's law or the Boyle–Mariotte law. Later, in 1687 in the ""Philosophiæ Naturalis Principia Mathematica"", Newton showed mathematically that if an elastic fluid consisting of particles at rest, between which are repulsive forces inversely proportional to their distance, the density would be directly proportional to the pressure, but this mathematical treatise is not the physical explanation for the observed relationship. Instead of a static theory a kinetic theory is needed, which was provided two centuries later by Maxwell and Boltzmann. This law was the first physical law to"
"Torricelli's law Torricelli's law, also known as Torricelli's theorem, is a theorem in fluid dynamics relating the speed of fluid flowing out of an orifice to the height of fluid above the opening. The law states that the speed of efflux, ""v"", of a fluid through a sharp-edged hole at the bottom of a tank filled to a depth ""h"" is the same as the speed that a body (in this case a drop of water) would acquire in falling freely from a height ""h"", i.e. formula_1, where ""g"" is the acceleration due to gravity (9.81 N/kg near the surface"
"that heat does not spontaneously flow from a colder body to a hotter. Other formulations followed quickly (for example, the second law was expounded in Thomson and Peter Guthrie Tait's influential work ""Treatise on Natural Philosophy"") and Kelvin in particular understood some of the law's general implications. The second Law was the idea that gases consist of molecules in motion had been discussed in some detail by Daniel Bernoulli in 1738, but had fallen out of favor, and was revived by Clausius in 1857. In 1850, Hippolyte Fizeau and Léon Foucault measured the speed of light in water and find"
"Law of the wall In fluid dynamics, the law of the wall states that the average velocity of a turbulent flow at a certain point is proportional to the logarithm of the distance from that point to the ""wall"", or the boundary of the fluid region. This law of the wall was first published by Theodore von Kármán, in 1930. It is only technically applicable to parts of the flow that are close to the wall (<20% of the height of the flow), though it is a good approximation for the entire velocity profile of natural streams. The logarithmic law"