Momentum equation

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The momentum equation is the second of the MHD equations . It ensures that pressure terms balance one another. It is usually expressed as:

\rho\frac{d \mathbf{v}}{d t}=-\nabla p+\frac{\left(\nabla\times\mathbf{B}\right)\times\mathbf{B}}{4\pi}

The momentum equation may be expressed in its conservative form:

\frac{\partial\left(\rho\mathbf{v}\right)}{\partial t}+\nabla\cdot\mathbf{T}=0

Where \mathbf{T} is the stress tensor :

\mathbf{T}=\rho\vec{\mathbf{v}}\vec{\mathbf{v}}+\left(p+\frac{B^{2}}{8\pi}\right)\vec{\vec{\mathbf{I}}}-\frac{\vec{\mathbf{B}}\vec{\mathbf{B}}}{4\pi}

This page was recovered in October 2009 from the Plasmagicians page on Momentum_equation dated 21:28, 10 April 2007.

Retrieved from "https://qed.princeton.edu/main/PlasmaWiki/Momentum_equation"
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