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# Calculus/Conversion Factors

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.

To convert to gallons from liters, multiply by 0.264.
To convert to Fahrenheit from Centigrade, multiply by 1.8 and add 32.

Since the equation is y = 9294.5x^(-1.141) when in metric, I would use the same formula,
but first x would be multiplied by 0.264.
Since the output is in degrees, multiply by 1.8 and add 32.

To do this directly, put in 0.264x for x.  This means taking 0.264 to the -1.141 and
multiplying by 9294.5 to get the constant.  I get 2030 for the answer, but this isn't
the last operation, so keep it as far as it goes for now.

To change the output to degrees, it becomes 3690, which is gotten by multiplying by 1.8,

This leads to the formula y = 1.8*9294.5[(x/.264)^(-1.141)] + 32.

What I get is y = 3660.6*(x^[-1.141]) + 32.  Is that what you get?

Calculus

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