diff options
Diffstat (limited to 'source/know/concept/boltzmann-equation')
| -rw-r--r-- | source/know/concept/boltzmann-equation/index.md | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/source/know/concept/boltzmann-equation/index.md b/source/know/concept/boltzmann-equation/index.md index d2631b2..9cb3bcd 100644 --- a/source/know/concept/boltzmann-equation/index.md +++ b/source/know/concept/boltzmann-equation/index.md @@ -12,7 +12,7 @@ layout: "concept" Consider a collection of particles, each with its own position $$\vb{r}$$ and velocity $$\vb{v}$$. We can thus define a probability density function $$f(\vb{r}, \vb{v}, t)$$ -describing the expected number of particles at $$(\vb{r}, \vb{v})$$ at time $$t$$. +describing the expected particle count at $$(\vb{r}, \vb{v})$$ at time $$t$$. Let the total number of particles $$N$$ be conserved, then clearly: $$\begin{aligned} @@ -205,9 +205,9 @@ $$\begin{aligned} = \rho \Expval{(\vb{v} \!-\! \vb{V}) (\vb{v} \!-\! \vb{V})} \end{aligned}$$ -This leads to the expected result, -where $$\nabla \cdot (\rho \vb{V}\vb{V})$$ represents the fluid momentum, -and $$\nabla \cdot \hat{P}$$ the viscous/pressure momentum: +This leads to the desired result, +where $$\nabla \cdot (\rho \vb{V}\vb{V})$$ is the fluid momentum, +and $$\nabla \cdot \hat{P}$$ is the viscous/pressure momentum: $$\begin{aligned} 0 |