how to fit a correlation to meassured data in excel

[themroc]

In the attached excel sheet (interpolation.xls) measured friction factor data are shown as a function of Reynolds. The data are for different packing densities. 30 = lowest packing 80 = highest packing.

As it can be seen the values are strongly decreasing with higher Reynolds number.
Applying the excel trend lines does not give a good fit.
The power function fits well until a Reynolds number of 100 but for higher values I can not find a suitable fit.
Can anyone propose a software package which is able to apply trendlines for such kind of curves.
What kind of mathematical equation would fit the data?
Ideally a two dimensial function which gives
f = f(reynolds; packing density)

Any sugestion apreciated

 

[Bribyk]

Use an linear trendline in Excel. Manipulate your raw data using a function that you think will linearize the correlation. Try a few functions, see how the linear trendline matches up (desired slope = 1:1) and revise your function to improve it.

 

[GregLocock]

It very much depends on what you are trying to do. Bribyk's approach is the best one if you are merely trying to interpolate using a function, but if you are trying to validate some underlying physics then you are better off normalising back to the theoretical curve, and then trying to explain the differences.

Having said that I rather think your difficulty is not so much in getting the shape vs Re, your packing density effect looks far more non linear on the log-log curve.

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[orenda1168]

If the cost doesn't bother you, look/get Tablecurve 2D from Systat. This runs about $500 and change, but is far and away the most complete curve fitting and analysis software available.

Orenda

 

[corus]

As Greg suggests take the log of both the x and y axes and plot those. You can fit an almost exact quadratic through this new data, from which you can tranpose the variables back to the original data, to obtain a formula.

corus

 

[GregLocock]

I fiddled around a bit and got a pretty good agreement, looks like the correction for the packing density is just log(packing density).

As Corus says a quadratic of log(Re) seems to be a reasonable fit.

However the error plot of what I have left is extremely complex, are those real data points?

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.