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Calculus/Formula Conversion

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Question
Hi,

I'm working on a problem that requires me to find the empirical relationship between reactor temperature T('C) and the flowrate of the cooling water mC (L/s).

The flow rates/x values are   25, 40, 55, 70, 90

The temperatures/y values are 237, 138, 96, 73, 55

Plugging the numbers into excel and adding a power trend line gives me a formula of y = 9294.5x^(-1.141) with an R^2 value of 1. I'm supposed to convert the above formula so that it can be used with degrees Fahrenheit instead of degrees Celsius and gallons/second instead of L/s.

I have tried everything to get a formula where I could plug in the x value in gallons/per second to get the value of Fahrenheit and convert back to degrees Celsius to compare with the results of the above mentioned formula but I cannot find a single equation that works.

What am I doing wrong? I'd really appreciate some help with this. Thanks a million in advance.

Answer
Hi Ari,
It would've been better if you showed me what you've done.
Anyway, your problem seems to be one of conversion. So, we have
y = 9294.5x^(-1.141)
Now, temperatures in Fahrenheit and Celsius are related by
C = 5(F - 32)/9
and
1 litre = 0.264 US gallons
Your new formula should then look like;
5(Y - 32)/9 = (9294.5)[(0.264X)^(-1.141)]
5(Y - 32)/9 = (9294.5) (0.264)^(-1.141) (X)^(-1.141)
Y - 32 = (9/5) (9294.5) (0.264)^(-1.141) (X)^(-1.141)
Y - 32 = 76462.49X^(-1.141)
Y = 32 + 76462.49X^(-1.141)

So give that a try.

Regards

Calculus

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Ahmed Salami

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