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cra-vg-derivadas.pgf
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cra-vg-derivadas.pgf
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% http://www.texample.net/tikz/examples/free-body-diagrams/
\def\tr{0.1}
\def\ts{0.6}
\def\al{1.3}
\def\n{1.6}
\def\I{0.3506} % -log(al)+log(m)/n = -log(al)+log(1-1/n)/n
\def\ti{0.4071}
\def\S{-0.1340}
\def\Sangle{-42}
\def\f1{0.8}
\begin{tikzpicture}[domain=-3:5, xscale=1.1, yscale=6, >=latex]
\draw[very thin,color=gray!30] (-3,0)
grid[xstep=0.5, ystep=0.1] (5,0.7);
\draw[->, line width=1pt] (-3,0) -- (5.25,0)
node[below] {$\log(\psi)$};
\draw[->, line width=1pt] (-3,0) -- (-3,0.75)
node[left] {$U(\psi)$};
\draw[color=green!30!black, thick, smooth]
plot[id=x, domain=-3:5]
function{\tr+(\ts-\tr)/(1+(\al*exp(x))**\n)**(1-1/\n)};
\node[left] (tr) at (-3,\tr) {$U_r$};
\node[left] (ts) at (-3,\ts) {$U_s$};
\draw[dashed] (\I,0) node[below] {$I$} -- (\I,\ti) -- (-3,\ti)
node[left] {$U_i$};
\draw[color=green!30!black, dashed]
plot[id=x, domain=-1.5:3]
function{\ti+\S*(x-\I)};
\draw [decorate,decoration={brace,amplitude=4pt}]
(-3.5,\tr) -- (-3.5,\ts) node [black,midway,left] {$\Delta$};
\draw[|<->|] (\I,\ti)++(1,0) arc (0:\Sangle:0.8 and 0.15);
\path (\I,\ti)++(0.5*1.5\Sangle/8:1)
node[right=-1pt] {$\tan^{-1}(S)$};
\node[anchor=base] (vg) at (1,0.8)
{$U(\psi) = U_r+\displaystyle\frac{U_s-U_r}{(1+(\alpha\psi)^n)^m}$};
\begin{scope}[yshift=-0.3cm,domain=-3:5, >=latex, yscale=3]
\draw[very thin,color=gray!30] (-3,-0.15)
grid[xstep=0.5, ystep=0.03] (5,0);
\draw[->, line width=1pt] (-3,-0.15) -- (5.25,-0.15)
node[below] {$x=\log(\psi)$};
\draw[->, line width=1pt] (-3,-0.15) -- (-3,0.03)
node[left] {$U'(x)$};
\draw[color=green!30!black, thick, smooth]
plot[id=x, domain=-3:5]
function{-(\ts-\tr)*\n*(1-1/\n)*\al**\n*exp(\n*x)*
(1+(\al*exp(x))**\n)**(-1+1/\n-1)} node[right] {};
\node[left] (z) at (-3,0) {$0$};
\draw[dashed] (\I,0) -- (\I,\S) -- (-3,\S) node[left] {$S$};
\node[anchor=base] (dvg) at (1,0.02)
{$U'(x) = -(U_s-U_r) \,n m\alpha^n
\exp\{nx\}(1+(\alpha\exp\{x\})^n)^{-m-1}$};
\end{scope}
\begin{scope}[yshift=-1.6cm,domain=-3:5, >=latex, yscale=1.75]
\draw[very thin,color=gray!30] (-3,0)
grid[xstep=0.5, ystep=0.05] (5,0.35);
\draw[->, line width=1pt] (-3,0) -- (5.25,0)
node[below] {$x=\log(\psi)$};
\draw[->, line width=1pt] (-3,-0.05) -- (5.25,-0.05)
node[below] {$r=2\sigma\cos(\delta)/(\rho g \psi)$};
\draw[->, line width=1pt] (-3,0) -- (-3,0.38) node[left] {$f(x)$};
\draw[color=green!30!black, thick, smooth]
plot[id=x, domain=-3:5]
function{\n*(1-1/\n)*\al**\n*exp(\n*x)*
(1+(\al*exp(x))**\n)**(-1+1/\n-1)};
\node[left] (z) at (-3,0) {$0$};
\node[anchor=base] (inte) at (1,0.32)
{$\displaystyle\int_{-\infty}^{\infty} nm\alpha^n
\exp\{nx\}(1+(\alpha\exp\{x\})^n)^{-m-1}\,\, dx=1$};
\draw[dashed] (\I,0) -- (\I,-2*\S);
\end{scope}
\begin{scope}[yshift=-1.8cm, xshift=-0.5cm, xscale=8, yscale=1.5]
\foreach \r/\x in {10/-2, 8/0, 6/2, 4/4, 2/5.5} {
\draw (\x/8,0) circle (\r/150);
\draw (\x/8,0) -- ++(\r/150,0);
}
\node[below right] (r) at (-2/8,0) {$r$};
\node[anchor=base] (d) at (0.2,-0.12) {tamanho de poros ($r$)};
\end{scope}
\end{tikzpicture}