Watertank

https://www.desmos.com/calculator/ik6czhzwax

A cylindrical bottle is filled to a level of 130 mm. At time t=0 (minutes) a hole is punched in the bottom, and water begins to flow out.  It takes exactly 192 seconds for the tank to empty. We instruct the class to record the times at which the water arrives at each of the marked levels and plot these points on a set of t-z axes.

We now use these data to embark upon a fascinating journey of discovery. First of all, we note that Newton’s laws predict that the points ought to lie along a parabola. Given that we find that the “best-fit” parabola does pass pretty well through the points.

As a visual check we find a way to transform the data into a set of points that ought to lie along a line—essentially we plot root z against t. That linear set of points is quite a sight.

But we noting an interesting discrepancy towards the end of the plot, and tracking that one down teaches us something about viscosity.