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Cell[CellGroupData[{
Cell["Primer on Log-Log and Log-Linear (semi-log) Plots", "Title"],

Cell[TextData[{
  "This notebook has been written in  ",
  StyleBox["Mathematica ",
    FontSlant->"Italic"],
  "by \n\n",
  StyleBox["Mark J. McCready\nProfessor and Chair of Chemical Engineering\n\
University of Notre Dame\nNotre Dame, IN 46556\nUSA",
    FontSize->14],
  "\n\n",
  ButtonBox["mjm@nd.edu",
    ButtonStyle->None],
  "\n",
  ButtonBox["http://www.nd.edu/~mjm/",
    ButtonData:>{
      URL[ "http://www.nd.edu/~mjm/"], None},
    ButtonStyle->"Hyperlink"],
  "\n\n\nIt is copyrighted to the extent allowed by which ever laws pertain \
to the World Wide Web and the Internet.\n\nI would hope that as a \
professional courtesy, this notice remain visible to other users. \nThere is \
no charge for copying and dissemination.   \n\nVersion: 6/19/00\nMore recent \
versions of this notebook may be available at:\n",
  Cell[BoxData[
      FormBox[
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Cell[CellGroupData[{

Cell["Motivation", "Subtitle"],

Cell[TextData[{
  "Once you have done dimensional analysis and produced 2-3 dimensionless \
groups or if you are just using someone else's correlation, you may find that \
you need to use or produce a graphical representation of the model.  \n\nIf \
the model is such that there are two parameters and they are linearly \
related, then you will be happy to plot the model on a regular (linear) axis \
plot and you the result.  Even if you cook up some kind of polynomial fit, a \
linear plot is appropriate.\n\nIf y = m x + b  or\n\ny = b0 + b1 ",
  Cell[BoxData[
      \(TraditionalForm\`x\)]],
  " + b2 ",
  Cell[BoxData[
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  "\n\nHowever, if the dimensionless groups related by a power law or \
exponential function, it is convenient to use log-log or semilog plots to \
show the results.\n\nThis notebook gives examples of how to do this and shows \
why it is useful."
}], "Text"]
}, Open  ]],

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Cell["Linear plots", "Subsubsection"],

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However, many times the natural behavior of the model is not linear \
or polynomial.  For example we will soon find that pressure driven flow in a \
pipe gives f=16/Re as an exact solution for laminar flow and f=0.079 f-.25 as \
an approximate relation for turbulent flow.  How can we plot these?\
\>", \
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For the turbulent relation, again, the plot is ugly.  However, we \
realize that both relations are power laws. That is, the functional form \
involves just a product of a coefficient and the variable to some power. \
(often times this is all we need). 
So consider the manipulation. \
\>", "Text"]
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Now we see that we have a linear relation if we take the log of \
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\>", "Text"],

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Cell["\<\
Now we have the desired lines, but who knows what the axes values \
are?  We cannot read these directly.

How about if we skew the axes to be in terms of the logs of the values, \
choose base 10 for convenience.\
\>", "Text"],

Cell[TextData[{
  "In ",
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    FontSlant->"Italic"],
  ", you probably need to load this package."
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Cell["\<\
Try this command to check what different commands mean..  \
??LogLinearPlot\
\>", "Text",
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Cell[BoxData[
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  CellLabelAutoDelete->True],

Cell[BoxData[
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            {" "},
            {GridBox[{
                  {\(LogLinearPlot(Graphics`Graphics`Private`fun_, 
                        Graphics`Graphics`Private`range_, 
                        Graphics`Graphics`Private`opts___) := 
                      ScaledPlot(Graphics`Graphics`Private`fun, 
                        Graphics`Graphics`Private`range, 
                        ScaleFunction \[Rule] {\(log\_10\)(#1) &, #1 &}, 
                        Graphics`Graphics`Private`tickopts(LogScale, 
                          Automatic, 
                          LogLinearPlot, {\(log\_10\)(#1) &, #1 &}, 
                          Flatten[{Graphics`Graphics`Private`opts}]), 
                        Graphics`Graphics`Private`scaleplotrange(
                          LogLinearPlot, 
                          Flatten[{Graphics`Graphics`Private`opts}]), 
                        Graphics`Graphics`Private`opts, 
                        Options[LogLinearPlot])\)}
                  },
                GridBaseline->{Baseline, {1, 1}},
                ColumnWidths->0.999,
                ColumnAlignments->{Left}]},
            {" "},
            {GridBox[{
                  {
                    RowBox[{\(Options[LogLinearPlot]\), "=", 
                      RowBox[{"{", 
                        RowBox[{
                          RowBox[{"AspectRatio", "\[Rule]", 
                            FractionBox["1", 
                              TagBox["\[Phi]",
                                (GoldenRatio&)]]}], 
                          ",", \(Axes \[Rule] Automatic\), 
                          ",", \(AxesLabel \[Rule] None\), 
                          ",", \(AxesOrigin \[Rule] Automatic\), 
                          ",", \(AxesStyle \[Rule] Automatic\), 
                          ",", \(Background \[Rule] Automatic\), 
                          ",", \(ColorOutput \[Rule] Automatic\), 
                          ",", \(Compiled \[Rule] True\), 
                          ",", \(DefaultColor \[Rule] Automatic\), 
                          ",", \(Epilog \[Rule] {}\), 
                          ",", \(Frame \[Rule] False\), 
                          ",", \(FrameLabel \[Rule] None\), 
                          ",", \(FrameStyle \[Rule] Automatic\), 
                          ",", \(FrameTicks \[Rule] Automatic\), 
                          ",", \(GridLines \[Rule] None\), 
                          ",", \(ImageSize \[Rule] Automatic\), 
                          ",", \(MaxBend \[Rule] 10.`\), 
                          ",", \(PlotDivision \[Rule] 30.`\), 
                          ",", \(PlotLabel \[Rule] None\), 
                          ",", \(PlotPoints \[Rule] 25\), 
                          ",", \(PlotRange \[Rule] Automatic\), 
                          ",", \(PlotRegion \[Rule] Automatic\), 
                          ",", \(PlotStyle \[Rule] Automatic\), 
                          ",", \(Prolog \[Rule] {}\), 
                          ",", \(RotateLabel \[Rule] True\), 
                          ",", \(Ticks \[Rule] Automatic\), 
                          ",", \(DefaultFont \[RuleDelayed] $DefaultFont\), 
                          ",", \(DisplayFunction \[RuleDelayed] \
$DisplayFunction\), ",", \(FormatType \[RuleDelayed] $FormatType\), 
                          ",", \(TextStyle \[RuleDelayed] $TextStyle\)}], 
                        "}"}]}]}
                  },
                GridBaseline->{Baseline, {1, 1}},
                ColumnWidths->0.999,
                ColumnAlignments->{Left}]}
            },
          GridBaseline->{Baseline, {1, 1}},
          ColumnAlignments->{Left}],
        Definition[ LogLinearPlot],
        Editable->False], TraditionalForm]], "Print"]
}, Open  ]],

Cell["Now our plot is straight.  ", "Text",
  CellLabelAutoDelete->True],

Cell[CellGroupData[{

Cell[BoxData[
    \(\(LogLinearPlot[13\ Log[x], {x, 1, 100}];\)\)], "Input",
  CellLabelAutoDelete->True],

Cell[GraphicsData["PostScript", "\<\
%!
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*)




(***********************************************************************
End of Mathematica Notebook file.
***********************************************************************)