From 93c8b6e86aeafb2f1b7f6b4d39049276ebbcc91c Mon Sep 17 00:00:00 2001 From: Prefetch Date: Wed, 5 May 2021 20:18:57 +0200 Subject: Expand knowledge base --- content/know/concept/euler-equations/index.pdc | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) (limited to 'content/know/concept/euler-equations/index.pdc') diff --git a/content/know/concept/euler-equations/index.pdc b/content/know/concept/euler-equations/index.pdc index cedfd93..0088d4f 100644 --- a/content/know/concept/euler-equations/index.pdc +++ b/content/know/concept/euler-equations/index.pdc @@ -21,7 +21,7 @@ There exist several forms, depending on the surrounding assumptions about the fluid. -## Incompressible fluid, uniform density +## Incompressible fluid In a fluid moving according to the velocity vield $\va{v}(\va{r}, t)$, the acceleration felt by a particle is given by @@ -123,9 +123,6 @@ $$\begin{aligned} } \end{aligned}$$ - -## Incompressible fluid, variable density - The above form is straightforward to generalize to incompressible fluids with non-uniform spatial densities $\rho(\va{r}, t)$. In other words, these fluids are "lumpy" (variable density), @@ -179,6 +176,10 @@ $$\begin{aligned} } \end{aligned}$$ +Usually, however, when discussing incompressible fluids, +$\rho$ is assumed to be spatially uniform, +in which case the latter equation is trivially satisfied. + ## References -- cgit v1.2.3