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| LaTeX Math Block |
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| anchor | rhophi |
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| alignment | left |
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|
d(\rho \, \phi) = \rho \, d \phi + \phi \, d\rho = \rho \, \phi \, \left( \frac{d \phi }{\phi} + \frac{d \rho }{\rho} \right)
= \rho \, \phi \, \left( \frac{1}{\phi} \frac{d \phi}{dp} \, dp + \frac{1}{\rho} \frac{d \rho}{dp} \, dp \right)
= \rho \, \phi \, (c_{\phi} \, dp + c \, dp) = \rho \, \phi \, c_t \, dp |
where
to arrive at:
| LaTeX Math Block |
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| anchor | pre_filnal |
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| alignment | left |
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| \rho \, \phi \, c_t \cdot \frac{\partial p}{\partial t} + \nabla \, ( \rho \, {\bf u}) = \rho \, \sum_k q_k(t) \cdot \delta({\bf r}-{\bf r}_k) |
| | LaTeX Math Block |
|---|
| anchor | qGamma |
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| alignment | left |
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| {\rm F}_{\Gamma}(p, {\bf u}) = 0 |
|
where
Then use the following equality:
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