“Navier–Stokes equations”的概念、定义、翻译、参考文献-科学参考

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:
$\begin{array}{l} ρ (\frac{\partial v_{x}}{\partial t} + v_{x} \frac{\partial v_{x}}{\partial x} + v_{y} \frac{\partial v_{y}}{\partial y} + v_{z} \frac{\partial v_{z}}{\partial z}) = ρ g_{x} - \frac{\partial p}{\partial x} + μ (\frac{\partial^{2} v_{x}}{\partial x^{2}} + \frac{\partial^{2} v_{x}}{\partial y^{2}} + \frac{\partial^{2} v_{x}}{\partial z^{2}}) \\ \begin{array}{l} ρ (\frac{\partial v_{y}}{\partial t} + v_{x} \frac{\partial v_{y}}{\partial x} + v_{y} \frac{\partial v_{y}}{\partial y} + v_{z} \frac{\partial v_{z}}{\partial z}) = ρ g_{y} - \frac{\partial p}{\partial y} + μ (\frac{\partial^{2} v_{y}}{\partial x^{2}} + \frac{\partial^{2} v_{y}}{\partial y^{2}} + \frac{\partial^{2} v_{y}}{\partial z^{2}}) \\ ρ (\frac{\partial v_{z}}{\partial t} + v_{x} \frac{\partial v_{z}}{\partial x} + v_{y} \frac{\partial v_{y}}{\partial y} + v_{z} \frac{\partial v_{z}}{\partial z}) = ρ g_{z} - \frac{\partial p}{\partial z} + μ (\frac{\partial^{2} v_{z}}{\partial x^{2}} + \frac{\partial^{2} v_{z}}{\partial y^{2}} + \frac{\partial^{2} v_{z}}{\partial z^{2}}) \end{array} \end{array}$

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.

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: $\begin{array}{l} ρ (\frac{\partial v_{x}}{\partial t} + v_{x} \frac{\partial v_{x}}{\partial x} + v_{y} \frac{\partial v_{y}}{\partial y} + v_{z} \frac{\partial v_{z}}{\partial z}) = ρ g_{x} - \frac{\partial p}{\partial x} + μ (\frac{\partial^{2} v_{x}}{\partial x^{2}} + \frac{\partial^{2} v_{x}}{\partial y^{2}} + \frac{\partial^{2} v_{x}}{\partial z^{2}}) \\ \begin{array}{l} ρ (\frac{\partial v_{y}}{\partial t} + v_{x} \frac{\partial v_{y}}{\partial x} + v_{y} \frac{\partial v_{y}}{\partial y} + v_{z} \frac{\partial v_{z}}{\partial z}) = ρ g_{y} - \frac{\partial p}{\partial y} + μ (\frac{\partial^{2} v_{y}}{\partial x^{2}} + \frac{\partial^{2} v_{y}}{\partial y^{2}} + \frac{\partial^{2} v_{y}}{\partial z^{2}}) \\ ρ (\frac{\partial v_{z}}{\partial t} + v_{x} \frac{\partial v_{z}}{\partial x} + v_{y} \frac{\partial v_{y}}{\partial y} + v_{z} \frac{\partial v_{z}}{\partial z}) = ρ g_{z} - \frac{\partial p}{\partial z} + μ (\frac{\partial^{2} v_{z}}{\partial x^{2}} + \frac{\partial^{2} v_{z}}{\partial y^{2}} + \frac{\partial^{2} v_{z}}{\partial z^{2}}) \end{array} \end{array}$ 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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