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| -rw-r--r-- | fig/bernoulli.tex | 42 | ||||
| -rw-r--r-- | ph2hat_zf.pdf | bin | 107154 -> 108251 bytes | |||
| -rw-r--r-- | ph2hat_zf.tex | 9 |
3 files changed, 50 insertions, 1 deletions
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 Binary files differindex e973c60..cf5a443 100644 --- a/ph2hat_zf.pdf +++ b/ph2hat_zf.pdf 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. \[ \Gamma = \oint \vec{v} \di{\vec{l}} \] |