diff options
Diffstat (limited to 'content/know/concept/euler-equations/index.pdc')
| -rw-r--r-- | content/know/concept/euler-equations/index.pdc | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/content/know/concept/euler-equations/index.pdc b/content/know/concept/euler-equations/index.pdc index 0088d4f..b531260 100644 --- a/content/know/concept/euler-equations/index.pdc +++ b/content/know/concept/euler-equations/index.pdc @@ -57,7 +57,7 @@ Next, we want to find another expression for $\va{f^*}$. We know that the overall force $\va{F}$ on an arbitrary volume $V$ of the fluid is the sum of the gravity body force $\va{F}_g$, and the pressure contact force $\va{F}_p$ on the enclosing surface $S$. -Using Gauss' theorem, we then find: +Using the divergence theorem, we then find: $$\begin{aligned} \va{F} @@ -91,7 +91,7 @@ $$\begin{aligned} The last ingredient is **incompressibility**: the same volume must simultaneously be flowing in and out of an arbitrary enclosure $S$. -Then, by Gauss' theorem: +Then, by the divergence theorem: $$\begin{aligned} 0 @@ -131,7 +131,7 @@ but the size of their lumps does not change (incompressibility). To update the equations, we demand conservation of mass: the mass evolution of a volume $V$ is equal to the mass flow through its boundary $S$. -Applying Gauss' theorem again: +Applying the divergence theorem again: $$\begin{aligned} 0 |