diff --git a/tex/header/preamble.tex b/tex/header/preamble.tex index 4a371a77f7d44940e9bda2ecbe08e4da189649a3..3d7739963ff1d240ea6b7cd42f54103ef7d2f76a 100644 --- a/tex/header/preamble.tex +++ b/tex/header/preamble.tex @@ -40,7 +40,7 @@ } % Abkürzunngen \newcommand{\diagramwidth}{0.9\linewidth} - +\newcommand{\Rey}{\operatorname{Re}_d} % weitere Befehle % Typografisches diff --git a/tex/main.tex b/tex/main.tex index 8a36a5241e70ee2072b13f9c3a06517045a282cd..71fc359051b59ace6a7c2a82d7c9a1aae52bd240 100644 --- a/tex/main.tex +++ b/tex/main.tex @@ -6,6 +6,7 @@ \maketitle % use \textinput as described in /header and _TEMPLATE \textinput{mesh} +\textinput{reynold} \textinput{diagrams} % \begin{appendices} % \textinput{some-appendix-section} diff --git a/tex/reynold.tex b/tex/reynold.tex new file mode 100644 index 0000000000000000000000000000000000000000..93a996bb27d18487be50a60e41ce55cdd3cbd2cd --- /dev/null +++ b/tex/reynold.tex @@ -0,0 +1,20 @@ +%! TEX program = lualatex + +\input{.maindir/tex/header/preamble-section} +% inputs the preamble only if necessary +\docStart +\section{Reynolds number} +In order to calculate the mean inflow velocity to achieve a specific Reynolds number, +consider the definition of the Reynolds number: +\begin{align*} + \Rey = \frac{\bar u d}{ν} +\end{align*} +where $d = \SI{0.1}{\metre}$ is the diameter of the cylinder and $ν = \SI{10e-3}{\square\metre\per\second}$ is the kinematic viscosity\footnote{\url{https://en.wikipedia.org/wiki/Viscosity#Kinematic_viscosity}}. +Therefore +\begin{align*} + \bar u = \frac{\Rey ν}{d} = \frac{\Rey · \SI{10e-3}{\square\metre\per\second}}{\SI{0.1}{\metre}} = \frac{\Rey}{100} \si{\metre\per\second} \\ + \bar u = \SI{0.2}{\metre\per\second} \quad \text{for } \Rey = 20 \\ + \bar u = \SI{1}{\metre\per\second} \quad \text{for } \Rey = 100 +\end{align*} +This can be changed the inlet velocity computation where a variable is used that is set in the file |scale|. +\docEnd