Bernoulli s theorem in fluid dynamics relation among the pressure velocity and elevation in a moving fluid liquid or gas the compressibility and viscosity internal friction of which are negligible and the flow of which is steady or laminar First derived 1738 by the Swiss mathematician Daniel Bernoulli the theorem states in effect that the total mechanical energy of the flowing fluid comprising the energy associated with fluid pressure the gravitational potential energy of elevation and the kinetic energy of fluid motion remains constant Bernoulli s theorem is the principle of energy conservation for ideal fluids in steady or streamline flow and is the basis for many engineering applications Bernoulli s theorem implies therefore that if the fluid flows horizontally so that no change in gravitational potential energy occurs then a decrease in fluid pressure is associated with an increase in fluid velocity If the fluid is flowing through a horizontal pipe of varying cross sectional area for example the fluid speeds up in constricted areas so that the pressure the fluid exerts is least where the cross section is smallest This phenomenon is sometimes called the Venturi effect after the Italian scientist G B Venturi 1746 1822 who first noted the effects of constricted chan Related Content Quizzes Physics and Natural Law All About Physics Quiz Media More Images More Articles On This Topic Contributors Article History HomeScienceMathematics Navier Stokes equation physics flow past a stationary solid sphere Related Topics See all media fluid mechanics Millennium Problem fluid flow See all related content Navier Stokes equation in fluid mechanics a partial differential equation that describes the flow of incompressible fluids The equation is a generalization of the equation devised by Swiss mathematician Leonhard Euler in the 18th century to describe the flow of incompressible and frictionless fluids In 1821 French engineer Claude Louis Navier introduced the element of viscosity friction for the more realistic and vastly more difficult problem of viscous fluids Throughout the middle of the 19th century British physicist and mathematician Sir George Gabriel Stokes improved on this work though complete solutions were obtained only for the case of simple two dimensional flows The complex vortices and turbulence or chaos that occur in three dimensional fluid including gas flows as velocities increase have proven intractable to any but approximate numerical analysis methods Euler s original equation in modern notation is velocity vector P is the fluid pressure is the fluid density and indicates the gradient where u is the fluid The Navier Stokes equation in modern notation is where u is the fluid velocity vector P is the fluid pressure is the fluid density is the kinematic viscosity and 2 is the Laplacian operator see Laplace s equation In 2000 whether smooth reasonable solutions to the Navier Stokes equation in three dimensions exist was designated a Millennium Problem one of seven mathematical problems selected by the Clay Mathematics Institute of Cambridge Massachusetts U S for a special award The solution for each Millennium Problem is worth 1 million Introduction Fast Facts Related Content More More Articles On This Topic Contributors Article History HomeSciencePhysicsMatter Energy geostrophic motion atmospheric science Print Cite Share Feedback geostrophic motion fluid flow in a direction parallel to lines of equal pressure isobars in a rotating system such as the Earth Such flow is produced by the balance of the Coriolis force q v caused by the Earth s rotation and the pressure gradient force The velocity of the flow is proportional to the gradient of the pressure and inversely proportional to latitude Although observed fluid motions are not strictly geostrophic large scale oceanic and atmospheric movements approach the ideal that is the geostrophic current usually represents the actual current within about 10 percent provided the comparison is made over large areas and there is little curvature in the isobars On a nonrotating Earth the pressure gradient force would cause the wind to blow directly from a region of high to one of low pressure across isobars Because the Earth does rotate however the Coriolis force deflects the wind toward parallelism with the isobars The Coriolis force deflects the wind to the right in the Northern Hemisphere and to the left in the Southern Hemisphere More From Britannica ocean current Geostrophic currents Near the surface friction between the air and the surface causes the wind to blow at less than a right angle to the pressure gradient Near the Equator where the Coriolis force is weak because it is a function of latitude the wind generally blows toward low pressure The geostrophic wind concept is useful in weather forecasting because it facilitates the mapping of wind streamlines in regions where wind observations are sparse and of isobars where pressure data are scanty See also gradient wind This article was most recently revised and updated by John P Rafferty Motog73 5G Launched With India s 1st Fastest Dimensity 930 SPONSORED BY ONLINE SHOPPING INDIA LEARN MOR Introduction streamline In fluid mechanics the path of imaginary particles suspended in the fluid and carried along with it In steady flow the fluid is in motion but the streamlines are fixed Where streamlines crowd together the fluid speed is relatively high where they open out the fluid is relatively still See also laminar flow turbulent flow This article was most recently revised and updated by Robert Curley Reynolds number Table of Contents Introduction Fast Facts Related Content Media More Images More Articles On This Topic Contributors Article History HomeSciencePhysicsMatter Energy Reynolds number Reynolds number Key People Related Topics Osborne Reynolds magnetic Reynolds number fluid flow See all related content Reynolds number in fluid mechanics a criterion of whether fluid liquid or gas flow is absolutely steady streamlined or laminar or on the average steady with small unsteady fluctuations turbulent Whenever the Reynolds number is less than about 2 000 flow in a pipe is generally laminar whereas at values greater than 2 000 flow is usually turbulent Actually the transition between laminar and turbulent flow occurs not at a specific value of the Reynolds number but in a range usually beginning between 1 000 to 2 000 and extending upward to between 3 000 and 5 000 In 1883 Osborne