My goal is to calculate the time of evaporation for water when this vase (below) is completely full. I understand that the simplest way would be to experimentally measure the evaporation time, however, I do not want to do that - I want to see if I can calculate it mathematically, and then compare it to the experimental value.
As you can see, the vase is not a perfect cylinder or sphere that could be easily modelled. I figured that one method to calculate the evaporation time mathematically would be to, using polynomial regression, model the shape of the vase on a software like GeoGebra, use integration (volumes of revolution) to turn my 2D model of the shape of the vase into a 3D one, and then use basic differential calculus to calculate the rate of evaporation.
I understand polynomial regression, and how the method of least squares could be applied - however, I am a little stuck as to how I can begin the method. Usually, because polynomial regression is used for obtaining trends from experimental data, which, a) come in data points as opposed to perfectly complete curves, and b) can easily be plotted on a coordinate axis to begin the polynomial regression, I am unsure of how to begin.
Any recommendations for a method to do this using freely available software would be much appreciated.
You could edit the image to have a horizontal line run through the vase, and then use any photo editor to identify points along the curve of the vase. Then, you could plot some of the pixel coordinates relative to the horizontal line on a new graph, and then, using polynomial regression, identify a piecewise function that best fits the points.
Needless to say, the more points you identify (on the curvature of the vase) and the more points you plot, the more accurate the result of your regression will be.