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Homework Help: Transposition of Formula, hopefully a simple one!

  1. Sep 17, 2010 #1
    1. The problem statement, all variables and given/known data

    The balance equation for a I/P system is:

    Pout = (KcY/Ax)*Iin + FsZ/Ax

    Where:

    Kc = 2500
    x+y = 0.1
    Z = 0.075
    A = 0.05

    Kc is the constant of proportionality relating to the input coil and Fs is the force exerted by the zero spring.

    a - Determine suitable values of y and x to give a straight line response of 'A' (shown on a graph I havnt put up here)

    2. Relevant equations

    Pout = (KcY/Ax)*Iin + FsZ/Ax

    Y = Mx + C

    3. The attempt at a solution

    According to the graph, the intercept (C) of the line runs through zero, thus Its safe to discount the FsZ/Ax part of the equation, leaving me with:

    Pout = (KcY/Ax)*In

    (Y=mx)

    According to the graph, reading values for Pout and In, these are:

    @ Pout = 1.0bar then In = 20mA.

    putting these values into the formula:

    1.0 = (KcY/Ax)*0.02

    Transposing gives

    1.0/0.02 = KcY/Ax

    thus

    50 = KcY/Ax

    and I know that A = 0.05 and Kc = 2500

    50 = 2500*Y / 0.05*Ax

    This is where I get a little confused as to the correct method of transposing to give x, I will run through the rest of my working now...

    50*0.05 = 2500*Y / x (moving the 0.05 from the bottom of one side to the top - becoming a multiple)

    thus

    2.5 = 2500*Y/X

    2.5/2500 = 0.001

    0.001 = Y / X

    as mentioned earlier on, x+y = 0.1
    so logically, y = 100-x
    inserting in the formula...

    0.001 = 100 - x / x

    shifting the 0.1 across..

    0.001 -0.1 = - x / x

    Heres the bit where I run into trouble, Im not sure how to deal with the -x / x in order to get it into one value,

    Im a little rusty when I get a further into transposition but this is driving me up the wall as its the key moment in the question which unlocks the value for further working.

    I tried multiplying each side by x to remove the fraction, ending up with:

    -0.099 * (x) = -x * (x)

    which I would then assume to give?

    -0.099x = -x2 ?????

    Like I said short of going in to see my tutor next week im a little stuck, if it does square the negative x how do I remove the x on the other side? argh!

    Looking back at the working Im not even entirely sure -0.099 is a correct value either but If someone could give guidance on how to deal with the x's that would be great....

    thanks in advance...
     
  2. jcsd
  3. Sep 17, 2010 #2

    Mark44

    Staff: Mentor

    I'm going to assume that your work up to here is correct. Your formatting makes it a little hard to read, since I have to parse KcY as meaning Kc * y, while Ax is A * x.

    Since Y * Kc/(Ax) = 50, then Y * Kc = 50Ax, and Y = 50A x /Kc.

    Assuming A and Kc are constants, there is a linear relationship between x and Y. (Why is Y capped by x not?)
     
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