From fcbcb7d8d6bd066cf6a4d1f085f0dc7291266011 Mon Sep 17 00:00:00 2001
From: Nao Pross <naopross@thearcway.org>
Date: Fri, 24 Apr 2020 15:54:22 +0200
Subject: Add diagram for Bernoulli

---
 fig/bernoulli.tex |  42 ++++++++++++++++++++++++++++++++++++++++++
 ph2hat_zf.pdf     | Bin 107154 -> 108251 bytes
 ph2hat_zf.tex     |   9 ++++++++-
 3 files changed, 50 insertions(+), 1 deletion(-)
 create mode 100644 fig/bernoulli.tex

diff --git a/fig/bernoulli.tex b/fig/bernoulli.tex
new file mode 100644
index 0000000..4f1916f
--- /dev/null
+++ b/fig/bernoulli.tex
@@ -0,0 +1,42 @@
+\begin{tikzpicture}
+    % axis
+    % \draw[->] (-1.5,-1.5) to ++(0,5) node[anchor=south] {\(y\)};
+    \draw[->] (-1,-1) to (8.5,-1) node[anchor=west] {\(x\)};
+    
+    % tube lines
+    \draw[] (0,2) to (1,2) to[out=0, in=180] (6,3) to (7,3);
+    \draw[] (0,0) to (1,0) to[out=0, in=180] (6,2) to (7,2);
+    
+    % opening ellipse for A1
+    \draw[blue!10, fill=blue!10] (0,.025) rectangle ++(.75,1.95);
+    \draw[fill=blue!10] (0,1) ellipse (.3 and 1);
+    % ellipse
+    \draw[dashed, fill=blue!10] (.75,1) ellipse (.3 and 1);
+    % closing ellipse
+    \draw[fill=blue!10] (7,2.5) ellipse (.2 and .5);
+    %% hide half of the ellipse and make dashed
+    \draw[blue!10, fill=blue!10] (6,2.025) rectangle ++(1,.95); 
+    \draw[dashed] (7,2.5) ellipse (.2 and .5);
+    % ellipse for A2
+    \draw[dashed, fill=blue!10] (6,2.5) ellipse (.2 and .5);
+    
+    % vectors
+    \draw[thick, ->] (-1,1) to node[near start, above, anchor=south] {\(v_1\)} ++(1,0) ;
+    \draw[thick, ->] (5,2.5) to node[near start, below, anchor=north] {\(v_2\)} ++(1,0) ;
+    
+    % heights
+    \draw[dotted] (0,1) to (2,1);
+    \draw[->] (1.5,-1) to node[pos=.3, anchor=west, right] {\(h_1\)} (1.5,1);
+    
+    \draw[dotted] (6,2.5) to (8,2.5);
+    \draw[->] (7.5,-1) to node[pos=.5, anchor=west, right] {\(h_2\)} (7.5,2.5);
+    
+    % areas
+    \draw[thick, blue] (0,.4) to [out=180, in=30] node[at end, anchor=east] {\(A_1\)} ++(-.5,-.4);
+    \draw[thick, blue] (6,2.2) to [out=210, in=80] node[at end, below, anchor=north] {\(A_1\)} ++(-.5,-.5);
+    
+    % other symbols
+    \node at (3,1.5) {\(\varrho\)};
+    \node at (-.7,2) {\(p_1\)};
+    \node at (7.5,3) {\(p_2\)};
+\end{tikzpicture}
diff --git a/ph2hat_zf.pdf b/ph2hat_zf.pdf
index e973c60..cf5a443 100644
Binary files a/ph2hat_zf.pdf and b/ph2hat_zf.pdf differ
diff --git a/ph2hat_zf.tex b/ph2hat_zf.tex
index f86e63d..0b7e65c 100644
--- a/ph2hat_zf.tex
+++ b/ph2hat_zf.tex
@@ -307,6 +307,12 @@ Der Term \(\varrho v^2 / 2\) wird \emph{dynamische Druck} genannt.
     p + \varrho g h + \frac{\varrho}{2} v^2 = (\text{Konstant})
 \]
 
+\begin{figure}[h] \centering
+    \resizebox{.9\linewidth}{!}{%
+        \input{fig/bernoulli}%
+    }
+\end{figure}
+
 \begin{remark}
 Bernoulli gilt f\"ur inkompressible Fluide, und gen\"ugt f\"ur Fl\"ussigkeite und Gase, sofern \(v \ll \) Schallgeschwidigkeit.
 \end{remark}
@@ -447,7 +453,8 @@ Das ist tats\"achlich \eqref{eqn:hagen-poiseuille} umformuliert.
 \]
 \end{definition}
 
-\begin{definition}[Zirkulation]
+\begin{definition}[Zirkulation] Ist ein Mass f\"ur die Wirbelst\"arke.
+Die Zirkulation ist eine makroskopische Gr\"osse und h\"ang vom Weg ab.
 \[
     \Gamma = \oint \vec{v} \di{\vec{l}}
 \]
-- 
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