Cauchy momentum equation

An example of convection. Though the flow may be steady (time-independent), the flow decelerates as it moves down the diverging duct (assuming incompressible or subsonic compressible flow), hence there is an acceleration happening over position.

The Cauchy momentum equation is a vector partial differential equation put forth by Cauchy that describes the non-relativistic momentum transport in any continuum. In convective (or Lagrangian) form it is written:

where $\rho$ is the density at the point considered in the continuum (for which the continuity equation holds), $\boldsymbol{\sigma}$ is the stress tensor, and $\mathbf{g}$ contains all of the body forces per unit mass (often simply gravitational acceleration). $\mathbf{u}$ is the flow velocity vector field, which depends on time and space.

单词	Cauchy momentum equation
释义	Cauchy momentum equation 英语百科 Cauchy momentum equation The Cauchy momentum equation is a vector partial differential equation put forth by Cauchy that describes the non-relativistic momentum transport in any continuum. In convective (or Lagrangian) form it is written: where $\rho$ is the density at the point considered in the continuum (for which the continuity equation holds), $\boldsymbol{\sigma}$ is the stress tensor, and $\mathbf{g}$ contains all of the body forces per unit mass (often simply gravitational acceleration). $\mathbf{u}$ is the flow velocity vector field, which depends on time and space.
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