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- DAlemberts_paradox abstract "In fluid dynamics, d'Alembert's paradox (or the hydrodynamic paradox) is a contradiction reached in 1752 by French mathematician Jean le Rond d'Alembert. D'Alembert proved that – for incompressible and inviscid potential flow – the drag force is zero on a body moving with constant velocity relative to the fluid. Zero drag is in direct contradiction to the observation of substantial drag on bodies moving relative to fluids, such as air and water; especially at high velocities corresponding with high Reynolds numbers. It is a particular example of the reversibility paradox.D’Alembert, working on a 1749 Prize Problem of the Berlin Academy on flow drag, concluded: "It seems to me that the theory (potential flow), developed in all possible rigor, gives, at least in several cases, a strictly vanishing resistance, a singular paradox which I leave to future Geometers [i.e. mathematicians - the two terms were used interchangeably at that time] to elucidate". A physical paradox indicates flaws in the theory.Fluid mechanics was thus discredited by engineers from the start, which resulted in an unfortunate split – between the field of hydraulics, observing phenomena which could not be explained, and theoretical fluid mechanics explaining phenomena which could not be observed – in the words of the Chemistry Nobel Laureate Sir Cyril Hinshelwood.According to scientific consensus, the occurrence of the paradox is due to the neglected effects of viscosity. In conjunction with scientific experiments, there were huge advances in the theory of viscous fluid friction during the 19th century. With respect to the paradox, this culminated in the discovery and description of thin boundary layers by Ludwig Prandtl in 1904. Even at very high Reynolds numbers, the thin boundary layers remain as a result of viscous forces. These viscous forces cause friction drag on streamlined objects, and for bluff bodies the additional result is flow separation and a low-pressure wake behind the object, leading to form drag.The general view in the fluid mechanics community is that, from a practical point of view, the paradox is solved along the lines suggested by Prandtl. A formal mathematical proof is lacking, and difficult to provide, as in so many other fluid-flow problems involving the Navier–Stokes equations (which are used to describe viscous flow).".
- DAlemberts_paradox thumbnail Alembert.jpg?width=300.
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- DAlemberts_paradox wikiPageWikiLink Adhémar_Jean_Claude_Barré_de_Saint-Venant.
- DAlemberts_paradox wikiPageWikiLink Aeronautics.
- DAlemberts_paradox wikiPageWikiLink Airfoil.
- DAlemberts_paradox wikiPageWikiLink Bernoullis_principle.
- DAlemberts_paradox wikiPageWikiLink Boundary-layer_thickness.
- DAlemberts_paradox wikiPageWikiLink Boundary_layer.
- DAlemberts_paradox wikiPageWikiLink Boundary_layer_thickness.
- DAlemberts_paradox wikiPageWikiLink Cambridge_University_Press.
- DAlemberts_paradox wikiPageWikiLink Category:Fluid_dynamics.
- DAlemberts_paradox wikiPageWikiLink Category:Paradoxes.
- DAlemberts_paradox wikiPageWikiLink Cavity_flow.
- DAlemberts_paradox wikiPageWikiLink Compressibility.
- DAlemberts_paradox wikiPageWikiLink Conservative_vector_field.
- DAlemberts_paradox wikiPageWikiLink Course_of_Theoretical_Physics.
- DAlemberts_paradox wikiPageWikiLink Cyril_Norman_Hinshelwood.
- DAlemberts_paradox wikiPageWikiLink Density.
- DAlemberts_paradox wikiPageWikiLink Dimensional_analysis.
- DAlemberts_paradox wikiPageWikiLink Dipole.
- DAlemberts_paradox wikiPageWikiLink Dissipation.
- DAlemberts_paradox wikiPageWikiLink Divergence_theorem.
- DAlemberts_paradox wikiPageWikiLink Drag_(physics).
- DAlemberts_paradox wikiPageWikiLink Drag_coefficient.
- DAlemberts_paradox wikiPageWikiLink Euclidean_vector.
- DAlemberts_paradox wikiPageWikiLink Euler_equations.
- DAlemberts_paradox wikiPageWikiLink Euler_equations_(fluid_dynamics).
- DAlemberts_paradox wikiPageWikiLink Flow_separation.
- DAlemberts_paradox wikiPageWikiLink Flow_velocity.
- DAlemberts_paradox wikiPageWikiLink Fluid.
- DAlemberts_paradox wikiPageWikiLink Fluid_dynamics.
- DAlemberts_paradox wikiPageWikiLink Fluid_mechanics.
- DAlemberts_paradox wikiPageWikiLink Form_drag.
- DAlemberts_paradox wikiPageWikiLink Garrett_Birkhoff.
- DAlemberts_paradox wikiPageWikiLink George_Gabriel_Stokes.
- DAlemberts_paradox wikiPageWikiLink Gradient.
- DAlemberts_paradox wikiPageWikiLink Gustav_Kirchhoff.
- DAlemberts_paradox wikiPageWikiLink Hermann_von_Helmholtz.
- DAlemberts_paradox wikiPageWikiLink Hydraulics.
- DAlemberts_paradox wikiPageWikiLink Incompressible.
- DAlemberts_paradox wikiPageWikiLink Incompressible_flow.
- DAlemberts_paradox wikiPageWikiLink Inviscid_flow.
- DAlemberts_paradox wikiPageWikiLink Irrotational.
- DAlemberts_paradox wikiPageWikiLink James_J._Stoker.
- DAlemberts_paradox wikiPageWikiLink Jean_le_Rond_dAlembert.
- DAlemberts_paradox wikiPageWikiLink John_Strutt,_3rd_Baron_Rayleigh.
- DAlemberts_paradox wikiPageWikiLink John_William_Strutt,_3rd_Baron_Rayleigh.
- DAlemberts_paradox wikiPageWikiLink Kelvin–Helmholtz_instability.
- DAlemberts_paradox wikiPageWikiLink Kinetic_energy.
- DAlemberts_paradox wikiPageWikiLink Kármán_vortex_street.
- DAlemberts_paradox wikiPageWikiLink Laminar_flow.
- DAlemberts_paradox wikiPageWikiLink List_of_things_named_after_Leonhard_Euler.
- DAlemberts_paradox wikiPageWikiLink Loschmidts_paradox.
- DAlemberts_paradox wikiPageWikiLink Ludwig_Prandtl.
- DAlemberts_paradox wikiPageWikiLink Method_of_matched_asymptotic_expansions.
- DAlemberts_paradox wikiPageWikiLink Navier–Stokes_equations.
- DAlemberts_paradox wikiPageWikiLink No-slip_boundary_condition.
- DAlemberts_paradox wikiPageWikiLink No-slip_condition.
- DAlemberts_paradox wikiPageWikiLink Normal_(geometry).
- DAlemberts_paradox wikiPageWikiLink Normal_vector.
- DAlemberts_paradox wikiPageWikiLink Parasitic_drag.
- DAlemberts_paradox wikiPageWikiLink Pergamon_Press.
- DAlemberts_paradox wikiPageWikiLink Physica_(journal).
- DAlemberts_paradox wikiPageWikiLink Physica_D.
- DAlemberts_paradox wikiPageWikiLink Physical_paradox.
- DAlemberts_paradox wikiPageWikiLink Potential_flow.
- DAlemberts_paradox wikiPageWikiLink Pressure.
- DAlemberts_paradox wikiPageWikiLink Prussian_Academy_of_Sciences.
- DAlemberts_paradox wikiPageWikiLink Reversibility_paradox.
- DAlemberts_paradox wikiPageWikiLink Reynolds_number.
- DAlemberts_paradox wikiPageWikiLink SIAM_Review.
- DAlemberts_paradox wikiPageWikiLink Scientific_consensus.
- DAlemberts_paradox wikiPageWikiLink Shear_stress.
- DAlemberts_paradox wikiPageWikiLink Sir_George_Stokes,_1st_Baronet.
- DAlemberts_paradox wikiPageWikiLink Skin_friction.
- DAlemberts_paradox wikiPageWikiLink Society_for_Industrial_and_Applied_Mathematics.
- DAlemberts_paradox wikiPageWikiLink Square_(algebra).
- DAlemberts_paradox wikiPageWikiLink Stagnation_point.
- DAlemberts_paradox wikiPageWikiLink Steady_flow.
- DAlemberts_paradox wikiPageWikiLink Stokes_flow.
- DAlemberts_paradox wikiPageWikiLink Stokes_law.
- DAlemberts_paradox wikiPageWikiLink Tangent.
- DAlemberts_paradox wikiPageWikiLink Tullio_Levi-Civita.
- DAlemberts_paradox wikiPageWikiLink Turbulence.
- DAlemberts_paradox wikiPageWikiLink Uriel_Frisch.
- DAlemberts_paradox wikiPageWikiLink Vector_calculus_identities.
- DAlemberts_paradox wikiPageWikiLink Vector_component.
- DAlemberts_paradox wikiPageWikiLink Velocity.
- DAlemberts_paradox wikiPageWikiLink Velocity_potential.
- DAlemberts_paradox wikiPageWikiLink Viscosity.
- DAlemberts_paradox wikiPageWikiLink Vortex.
- DAlemberts_paradox wikiPageWikiLink Vortex_street.
- DAlemberts_paradox wikiPageWikiLink Vorticity.