For a physicist, Albert Einstein (1879-1955) took a remarkable interest in physical chemistry. His doctoral thesis, submitted in 1905, was concerned with determining the dimensions of molecules. And his famous paper from the same year on Brownian motion has at its core the molecular-kinetic theory, a cornerstone of physical chemistry. In both these works, and […]Einstein and the Avogadro Number
For those of you who may not be familiar with how to do this, here is a video on how to plot graphs (and trend lines) on a spreadsheet:
For my students there are a few things that need to be added:
- Don’t delete the legend as he does; move it to the bottom of the graph (an option when you right click the legend.)
- You’ll need to include the R2 coefficient along with the trend line equation; that option is included when you set up the trend line.
- I prefer you look at polynomial regression last rather than just after linear. (Linear is obviously where you start.)
- Add major grid lines to the x-axis (same place as when you add the x-axis legend.)
The use of least squares regression and curve fitting is well established in the applied sciences. It is discussed in detail in the monograph Least Squares Analysis and Curve Fitting. Most analyses of this type, however, are done with only one independent variable (the classic linear fit is a good example of this.)
For some problems it is necessary to consider two or more independent variables (a recent example is here.) A way to perform regression on such data is to use the LINEST function, which can be used for linear/planar types of correlations. It can be found in most of the current spreadsheet packages. It is tricky to use; about the only way to illustrate its use is through a video, and one from Dr. Todd Grande is featured here.
Our main fluid mechanics laboratory page is here. Other resources relating to this laboratory is here:
- Fluid Flow in Pipes, Losses and Flow Metering (instructor’s handout.)
- Compressible Flow Through Nozzles. A look at flow with compressible fluids such as air.
- Getting the Reynolds Number Right. Messing up this calculation is an error I see too often; this should help.
- Valve Loss Study. Although this was with compressible fluids, the basic concepts are the same.
In the pressure gauge testing lab experiment, one of the requirements is that the “outliers” in the data are determined and excised from the analysis. One way of doing that is to apply Chauvenet’s Criterion. Below is a video of how that’s done and who Chauvenet was.
Note: he butchers the pronunciation of Chauvenet, sorry.