Transposition of Formula, hopefully a simple one

[cliopete]

Homework Statement

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)

Homework Equations

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

Y = Mx + C

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, I am 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 into see my tutor next week I am 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 I am 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...

 

[Mark44]

Homework Statement

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)

Homework Equations

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

Y = Mx + C

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

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 K_c * y, while Ax is A * x.

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

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

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, I am 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 into see my tutor next week I am 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 I am 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...