Grade 11: Water Tank

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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.

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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.

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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.

Teacher manual