# How to create a plot with normalized axis?

**URL:** <https://community.wolfram.com/t/how-to-create-a-plot-with-normalized-axis/16526>\
**Category:** Questions\
**Tags:** graphics-and-visualization\
**Created:** [August 4, 2020, 8:47pm UTC](https://community.wolfram.com/t/how-to-create-a-plot-with-normalized-axis/16526 "2020-08-04T20:47:05Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![mathematica4](https://avatars.discourse-cdn.com/v4/letter/m/ce73a5/32.png) [@mathematica4](https://community.wolfram.com/u/mathematica4)\
**Post date:** [August 4, 2020, 8:47pm UTC](https://community.wolfram.com/t/how-to-create-a-plot-with-normalized-axis/16526/1 "2020-08-04T20:47:05Z")

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**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! 🙂

_With kind regards, MM_

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<div class="post-metadata">

**Author:** ![rohitnamjoshi](https://avatars.discourse-cdn.com/v4/letter/r/f1d935/32.png) [@rohitnamjoshi](https://community.wolfram.com/u/rohitnamjoshi)\
**Post date:** [August 4, 2020, 9:24pm UTC](https://community.wolfram.com/t/how-to-create-a-plot-with-normalized-axis/16526/2 "2020-08-04T21:24:42Z")

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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

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<div class="post-metadata">

**Author:** ![mathematica4](https://avatars.discourse-cdn.com/v4/letter/m/ce73a5/32.png) [@mathematica4](https://community.wolfram.com/u/mathematica4)\
**Post date:** [August 5, 2020, 7:47am UTC](https://community.wolfram.com/t/how-to-create-a-plot-with-normalized-axis/16526/3 "2020-08-05T07:47:21Z")

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Thanks for the fast reply! 😉 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}]

```

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<div class="post-metadata">

**Author:** ![yhjack99](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/yhjack99/32/38072_2.png) [@yhjack99](https://community.wolfram.com/u/yhjack99)\
**Post date:** [August 5, 2020, 12:20pm UTC](https://community.wolfram.com/t/how-to-create-a-plot-with-normalized-axis/16526/4 "2020-08-05T12:20:53Z")

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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.

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<div class="post-metadata">

**Author:** ![rohitnamjoshi](https://avatars.discourse-cdn.com/v4/letter/r/f1d935/32.png) [@rohitnamjoshi](https://community.wolfram.com/u/rohitnamjoshi)\
**Post date:** [August 5, 2020, 1:52pm UTC](https://community.wolfram.com/t/how-to-create-a-plot-with-normalized-axis/16526/5 "2020-08-05T13:52:39Z")

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