How to plot this the streamlines xy=C by latex?

How to plot this the streamlines xy=C by latex? I attached my code but it does not generate the wanted figure.

this is my code

\documentclass[tikz,border=10pt,multi]{standalone}
\usetikzlibrary{shapes.symbols}

\makeatletter

\usepackage{pgfplots}
\makeatother

\begin{document}

\begin{tikzpicture}
\begin{axis}[
axis lines = left,
xlabel = $x$,
ylabel = {$f(x)$},
]
%Below the red is defined
domain=-2:2,
samples=20,
color=red,
]
{ 1/x};
\addlegendentry{$xy=-1$}
%Here  is defined
domain=-2:2,
samples=20,
color=green,
]
{-3/x};
\addlegendentry{$xy=3$}
domain=-2:2,
samples=20,
color=green,
]
{5/x};
\addlegendentry{$xy=-5$}

\end{axis}
\end{tikzpicture}

\end{document}


Here I present a solution using non-linear spacing that also works for quite low values for C or "high" values for Max (see code). For example test with values 0.1, 0.2 and 0.3 respectively or a Max value of 10. They work perfectly fine using only 22 samples per (full) line.

For details on how the solution works, please have a look at the comments in the code.

% used PGFPlots v1.16
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
% load library to use a "cool" cycle list'
\usetikzlibrary{
pgfplots.colorbrewer,
}
\pgfplotsset{
% use this compat' level or higher to use the advanced positioning
% for the axis labels
compat=1.3,
/pgf/declare function={
% declare a variable to store the min and max value for the function
Max=5;
% declare the function to use
f(\C,\x) = \C/\x;
%
% -----------------------------------------------------------------
% calculate the lower and upper boundaries (the domain values)
lb(\C) = sqrt(\C);
ub = Max;
%
%%% non-linear spacing: <https://stackoverflow.com/a/39140096/5776000>
% "non-linearity factor"
a = 1.0;
% function to use for the non-linear spacing
Y(\x) = exp(a*\x);
% rescale to former limits
X(\C,\x)  = (Y(\x) - Y(lb(\C)))/(Y(ub) - Y(lb(\C))) * (ub - lb(\C)) + lb(\C);
% -----------------------------------------------------------------
},
% load a "cool" cycle list
cycle list/Blues-5,
}
\begin{document}
\begin{tikzpicture}[
% define a style for the plot labels
Label/.style={
node font=\tiny,
black,
pos=#1,
},
]
\begin{axis}[
% axis lines should be centered
axis lines=center,
% set axis labels
xlabel={$x$},
ylabel={$f(x)$},
% set them right and above the axis lines, respectively
xlabel style={
at={(xticklabel* cs:1)},
anchor=west,
},
ylabel style={
at={(yticklabel* cs:1)},
anchor=south,
},
% axis unit ratio should be the same for both axis lines
axis equal image=true,
% don't show any ticks (and tick labels)
ticks=none,
% the lines should be smooth'
smooth,
% when using the non-linear spacing approach you don't need that much samples
samples=11,
%        % ---------------------------------------------------------------------
%        % for debugging purposes only
%        % ---------------------------------------------------------------------
%        % add small marks to the lines
%        every axis plot post/.append style={
%            mark=*,
%            mark size=0.3pt,
%        },
%        % ---------------------------------------------------------------------
]

% first draw the lines for $C = 0$
\pgfplotsinvokeforeach {0} {
% the horizontal line
% used forget plot' so the cycle list index' isn't increased
node [Label=0.4,above] {$C = #1$}
node [Label=0.6,above] {$C = #1$}
;
% the vertical line
node [Label=0.25,left] {$#1$}
node [Label=0.75,left] {$#1$}
;
}

% define a length for the shift of the plot labels
% (using "above left" and similar causes the labels to be
%  "too far away" from the plot they belong to and are almost
%  *in* the next plot)
\pgfmathsetlengthmacro{\Shift}{3pt}

% define a factor to enlarge the domain to get the parabolic effect
% of the end points of the different "C" plots
% (for linear spacing use the value 0.25)
\pgfmathsetmacro{\Factor}{0.01}

% now draw plots for $C > 0$
\pgfplotsinvokeforeach {1,2,3} {
% to do so we split each line into two part
% this is advantage because of the symmetry of the lines and
% thus we can avoid the need for a lot of "samples" in the steep
% parts of the curve.
%
% -----------------------------------------------------------------
% linear spacing approach
% -----------------------------------------------------------------
%                node [Label=0,shift={(\Shift,\Shift)}] {$+#1$};
%            % the steep parts can be drawn using a parametric plot
%
%                node [Label=1,shift={(-\Shift,\Shift)}] {$-#1$};
%
%                node [Label=1,shift={(-\Shift,-\Shift)}] {$+#1$};
%
%                node [Label=0,shift={(\Shift,-\Shift)}] {$-#1$};

% -----------------------------------------------------------------
% non-linear spacing approach
% -----------------------------------------------------------------
node [Label=0,shift={(\Shift,\Shift)}] {$+#1$};
% the steep parts can be drawn using a parametric plot

node [Label=0,shift={(-\Shift,\Shift)}] {$-#1$};

node [Label=0,shift={(-\Shift,-\Shift)}] {$+#1$};

node [Label=0,shift={(\Shift,-\Shift)}] {$-#1$};
}

\end{axis}
\end{tikzpicture}
\end{document}


@Barry -- There's a lot going on in your stagnation point flow, but here's a start, with lots more work on labels and arrowheads needed.

\documentclass[tikz,border=10pt,multi]{standalone}
\usetikzlibrary{shapes.symbols}

\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}
\begin{axis}[
axis x line=center,
axis y line=center,
xlabel = $x$,
ylabel = {$y$},
ymax=3,
ymin=-3,
ticks=none,
]
\node[right] at (-2,2) {$C=-2$};
\node[right] at (-0.7,0.2) {$C=0$};

%Below the red is defined
domain=-2:-0.1,
samples=50,
color=red,
]
{1/x};
domain=0.1:2,
samples=50,
color=red,
]
{(1/x)};
domain=-2:-0.1,
samples=50,
color=red,
]
{ -1/x};
domain=0.1:2,
samples=100,
color=red,
]
{(-1/x)};

% Now the teal
domain=-2.:-0.1,
samples=50,
color=teal,
]
{(0.5/x)};
domain=0.1:2,
samples=50,
color=teal,
]
{(0.5/x)};
domain=-2:-0.1,
samples=100,
color=teal,
]
{ -0.5/x};
domain=0.1:2,
samples=50,
color=teal,
]
{(-0.5/x)};

%Here green  is defined
domain=-2:-0.1,
samples=50,
color=green,
]
{-2/x};
domain=-2:-0.1,
samples=50,
color=green,
]
{2/x};
domain=0.1:2,
samples=50,
color=green,
]
{-2/x};
domain=0.1:2,
samples=50,
color=green,
]
{-2/x};

\end{axis}
\end{tikzpicture}

\end{document}
`

• Does anyone know how to do the arrowheads? – Barry Jun 2 '18 at 2:05
• There are some solutions in the questions on this board, but there may be other approaches. I did not have time to investigate in detail. – John Jun 2 '18 at 2:22
• I do not know why the label $\node[right] at (-2,2) {$C=-2$}; \node[right] at (-0.7,0.2) {$C=0\$}; does not appear when i generated the code. – Barry Jun 2 '18 at 6:32