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单词 Navier–Stokes equations
释义
Navier–Stokes equations

Chemical Engineering
  • A set of mathematical expressions used to study the motion of fluids. They are expressed in terms of velocity gradients for a Newtonian fluid with constant density and gradient. Using Cartesian or rectangular coordinates, the equations represent inertia of the left-hand side and body force, pressure, and viscous terms of the right-hand side:

    ρ(vxt+vxvxx+vyvyy+vzvzz)=ρgxpx+μ(2vxx2+2vxy2+2vxz2)ρ(vyt+vxvyx+vyvyy+vzvzz)=ρgypy+μ(2vyx2+2vyy2+2vyz2)ρ(vzt+vxvzx+vyvyy+vzvzz)=ρgzpz+μ(2vzx2+2vzy2+2vzz2)

    The equations can also be written using cylindrical and spherical coordinates. The solutions to the equations are called velocity fields or flow fields. The equations were developed by Claude-Louis Navier (1785–1836) in 1822, and developed further by George Stokes (1819–1903), and find many applications including the study of the flow of fluids in pipes and over surfaces.


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