I Empirical equation from two variables (1 input and 1 output)

[AligatorAmy]

Hi,
I have empirical data from my experiments.
There are 2 columns of data (2 interdependent variables- temperature and viscosity)..
1 column (temperature) is input variable (temp. of tested material, once it was melted, it was gradually increased during the experiment).
1 column (viscosity) is output variable (viscosity was decreasing as the input temperature was increasing).

I am looking for simple method to obtain the empirical equation, so once I hand over this data, someone can use the equation to calculate the change in viscosity for a given change of temperature.

I tried Excel (2010), e.g. regression, but I am still not sure how can I do it.
Please help. Regards.

 

[eys_physics]

It would probably help if you could post a plot of the viscosity versus temperature, since at at least I don't know how the slightest idea about how your data look like.

However, one thing to try is to plot the logarithm of the viscosity versus temperature. If the viscosity decreases exponentially you should see a straight line.

 

[AligatorAmy]

@eys_physics
Thank you for your reply. I send attached the plot in jpeg format.

 

[eys_physics]

I recommend to put $y=log(v)$ where #v# is the viscosity. Do then a polynomial regression of $y$ versus $T$. It will give you a polynomial $p(T)$.
I believe a linear or quadratic polynomial is enough. Finally, you have that $v=\exp(p(T))$.

 

[mfb]

Just based on the shape, something like a ln(b e^-cx+f e^-dx) with free parameters a,b,c,d,f should fit. I'm not sure how well-motivated that would be in terms of physics.