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Little math help here?

  1. Apr 26, 2010 #1
    Hey guys, I am a sophomore college student studying Aerospace Engineering and I am doing an experiment, and i ran into a little math problem that i can't seem to visualize properly.

    I have a y axis where which is a measure of pressure (from 0~200 bars), but expressed in voltages (1 to 5 volts).

    In order to properly analyze the results, i have to linearly transform the 1~5 volt scale to a 0~200 bar scale.

    I know it involves simple pre-calculus (with the y=mx+b) stuff but I just can't remember whatever I did in high school.

    Can anyone help me out here?

    Thanks in advance
     
  2. jcsd
  3. Apr 26, 2010 #2

    CompuChip

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    The formula y = mx + b you gave is for a straight line, i.e. a linear dependence. For this application, let me rename y to P (for pressure) and x to V (for voltage): P = m V + b.
    What you can do now, is simply plug in two points that you want to correspond. For example, if 1 volt corresponds to 0 bar, set V = 1, P = 0 to get
    0 = m 1 + b = m + b
    Take another point, for example to let 5 volts correspond to 500 bar, set V = 5, P = 500:
    500 = 5m + b.

    This gives you two equations from which you can solve m and b (for example, the first one gives you b = -m, plugging that into the second one produces 500 = 5m - m = 4m and then you can find m).

    (Note that there are faster ways, such as calculating m = delta P / delta V = (200 - 0) / (5 - 1) = 200 / 4 = 50 and then plugging in one point, but this one is more general).
     
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