Grade 11: Water Tank
I bring a plastic pop bottle with a small hole at the base, and horizontal lines marked on the side from z=0 to 130 mm. Since the bottle is cylindrical, basic physics tell us that the z-t graph should be a parabola. We use technology to calculate a best-fit parabola and the fit we obtain seems to be pretty good.
However we have reasons to worry about the fit at the very end when the water flows out slowly, so we find a way to “take square roots” and fit a straight line to the transformed data. The lines gives us much better visual evidence and our unease is confirmed––we find the right-hand end point to be an outlier. A discussion about liquid viscosity gives us an understanding of the cause of this.
We throw away the “outlier” and get an even better straight-line fit to the remaining points. This new line gives us a more accurate estimate of how long it “ought” to have taken to empty the tank. There are interesting lessons here in the scientific method.