Temperature/Pressure conversion for NH3

[rcguy111]

I am working on a conversion equation to put into the PLC that is running our refrigeration system. I have found the equation to convert temp to pressure, but i am struggling on finding the inverse of this equation. Any advice on a formula or method would be greatly appreciated.
y = .000044x3 + 0.0065x2 + 0.730x + 15.7

 

[rcguy111]

I am put a chart into excel but the new equation for pressure to temperature is not working correctly when I plug the original points back into it. It has a deviation of 150 degrees at the high end of the scale. Am I correct in assuming that the inverse of temp to pressure equation would give me the pressure to temp equation?

 

[Tedjn]

How did you find the inverse equation? Your temperature to pressure formula is a general cubic equation, and while it's possible to find x in terms of y via the cubic equation, it would be too long and tedious; moreover, you have to deal with the possibility that sometimes there may be more than one temperature for each pressure value (at least given by your equation). If your given formula was interpolated in the first place, you may as well just interpolate again in the reverse.

 

[rcguy111]

Yeah that is why I have tried it in excel in the same fashion I achieved the original equation. I was having difficulty with it and the deviation of the new equation was massive. so i tried multiple little additions to the equation. I found that my scientific notation was not precise enough so I increased my decimal places and developed an equation that has a max deviation of 2.5 degrees. It was a user problem. Thank you for the help. This will go from pressure to temperature...

y = -6.68E-08x4 + 4.60E-05x3 - 1.19E-02x2 + 1.70E+00x - 2.51E+01

 

[userpresley]

If you don't mind sharing your formula "y = -6.68E-08x4 + 4.60E-05x3 - 1.19E-02x2 + 1.70E+00x - 2.51E+01" what units are the variables y and x ?.

y is pressure in ?
x is temperature in ?

Kind Regards

 

[Bill Simpson]

See what the max deviation is on this

x= -49.242424242424235 - 0.516472181892512/(5.090996*10^-7 + 5.2272*10^-8*y + 5.2272*10^-8*sqrt(326.78516758494044 + 19.478864401591675*y + y^2))^(1/3) + 6012.882772606816*(5.090996*10^-7 + 5.2272*10^-8*y + 5.2272*10^-8*sqrt(326.78516758494044 + 19.478864401591675*y + y^2))^(1/3)