write about reynold number

still need to mention that the change has no effect

tex/header/preamble.tex

@@ -40,7 +40,7 @@
 }
 % Abkürzunngen
 \newcommand{\diagramwidth}{0.9\linewidth}
-
+\newcommand{\Rey}{\operatorname{Re}_d}
 % weitere Befehle
 
 % Typografisches

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}

tex/reynold.tex

+%! 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