Thinking of a vector field as a 2-form instead, a closed vector field is one whose derivative ( divergence ) vanishes, and is called an incompressible flow ( sometimes solenoidal vector field ).
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Most problems in incompressible flow involve only two unknowns : pressure and velocity, which are typically found by solving the two equations that describe conservation of mass and of linear momentum, with the fluid density presumed constant.
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For ships, unlike aircraft, one deals with incompressible flows, where change in water density is negligible ( a pressure rise close to 1000kPa leads to a change of only 2 3 kg / m 3 ).
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In fluid mechanics or more generally continuum mechanics, "'incompressible flow "'( flow in which the material density is constant within a fluid parcel an infinitesimal volume that moves with the flow velocity.
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The fundamental requirement for incompressible flow is that the density, \ rho, is constant within an infinitesimal volume, " dV ", which moves at the flow velocity "'u " '.
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Flandro has coauthored several textbooks including : " Basic Aerodynamics : Incompressible Flow " with Howard McMahon and Robert L . Roach of Georgia Tech, and " Combustion Instability in Solid Propellant Rockets " with Edward W . Price of Georgia Tech.
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And so beginning with the conservation of mass and the constraint that the density within a moving volume of fluid remains constant, it has been shown that an equivalent condition required for incompressible flow is that the divergence of the flow velocity vanishes.
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The boundary can be traveling in the medium, or it can be stationary while the medium flows along it, or they can both be moving, with different isothermal, compressibility effects will be small and simplified incompressible flow equations can be used.
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In D2Q9 and D3Q19, it is shown below for an incompressible flow in continuous and discrete form where " D ", " R ", and " T " are the dimension, universal gas constant, and absolute temperature respectively.
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In 1989 he completed his influential first book, " Finite Element Methods for Viscous Incompressible Flows : A Guide to Theory, Practice and Algorithms, " ISBN 978-0-12-307350-1, which according to Google scholar has over 400 citations as of March 2009.
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