How to create a plot with normalized axis?

Questions
1

Hi Community,

i need your help for my problem:

v[y_, w_] := v0 (Exp[w y/h] - 1)/(Exp[w] - 1)
h = 5;
v0 = 10;
Manipulate[Plot[v[y, w], {y, 0, 1}], {w, -10, 10}]

The plot should have axes with v/v0 and y/h. So the axes are in the range between 0 and 1 (and they should be fixed).

Hope you can help me! :slight_smile:

With kind regards, MM

2

You can fix the plot range by adding the following option to Plot

PlotRange -> {{0, 1}, {0, 1}}

Not sure what you mean by

have axes with v/v0 and y/h

3

Thanks for the fast reply! :wink: Maybe I should explain my problem better.

v[y_, w_] := v0 (Exp[w y/h] - 1)/(Exp[w] - 1) (* Velocity *)
w; (* Dimensionless Number *)
h = 5;  (* Height of the Channel *)
v0 = 10; (* Velocity at the Beginning *)
Manipulate[
 Plot[v[y, w], {y, 0, h}, PlotRange -> {{0, 1}, {0, 1}}, 
  AxesLabel -> {"\!\(\*FractionBox[\(y\), \(h\)]\)", 
    "\!\(\*FractionBox[\(v\), \(v0\)]\)"}], {w, -10, 10}]

So, I have a fluid with a velocity at the beginning of v0 in a channel with the height h. As you can see in the term with the exponential functions, if y → h, then the term → 1.

Now I want a plot with normalized axis (look at my new code) v/v0 (Range: 0 to 1) and y/h (Range: 0 to 1). I also tried to use Rescale (just for the y/h axis), but it didn’t work:

Manipulate[
 Plot[v[y, w], Rescale[{y, 0, h}, {0, 1}], 
  PlotRange -> {{0, 1}, {0, 1}}, 
  AxesLabel -> {"\!\(\*FractionBox[\(y\), \(h\)]\)", 
    "\!\(\*FractionBox[\(v\), \(v0\)]\)"}], {w, -10, 10}]
4

I think you should define v0 and h first and then
define a normalized v say called vnorm which is your v /v0 and plot vnorm instead of v.

5

Or Plot[v[y, w] / v0, ...]