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authorPrefetch2021-04-08 16:49:46 +0200
committerPrefetch2021-04-08 16:49:46 +0200
commit966048bd3594eac4d3398992c8ad3143e290303b (patch)
treee24f5aac65abfff9f80200ceb34f00676a82913d /content/know/concept/euler-equations/index.pdc
parent8044008e45f87b95d7a8c9f0fce1847ceedfb09a (diff)
Expand knowledge base, add /sources/
Diffstat (limited to 'content/know/concept/euler-equations/index.pdc')
-rw-r--r--content/know/concept/euler-equations/index.pdc4
1 files changed, 2 insertions, 2 deletions
diff --git a/content/know/concept/euler-equations/index.pdc b/content/know/concept/euler-equations/index.pdc
index 37d2fea..cedfd93 100644
--- a/content/know/concept/euler-equations/index.pdc
+++ b/content/know/concept/euler-equations/index.pdc
@@ -149,7 +149,7 @@ to which we apply a vector identity:
$$\begin{aligned}
0
= \dv{\rho}{t} + \nabla \cdot (\rho \va{v})
- = \dv{\rho}{t} + \va{v} \cdot \nabla \rho + \rho (\nabla \cdot \va{v})
+ = \dv{\rho}{t} + (\va{v} \cdot \nabla) \rho + \rho (\nabla \cdot \va{v})
\end{aligned}$$
Thanks to incompressibility, the last term disappears,
@@ -159,7 +159,7 @@ $$\begin{aligned}
\boxed{
0
= \frac{\mathrm{D} \rho}{\mathrm{D} t}
- = \dv{\rho}{t} + \va{v} \cdot \nabla \rho
+ = \dv{\rho}{t} + (\va{v} \cdot \nabla) \rho
}
\end{aligned}$$