Passage I

In 3 studies, students found the rate, R, at which water flowed through each of several holes in a water-filled cylinder. They also measured the horizontal distance, L, spanned by each stream of water (see Figure 1).

The students tested 3 cylinders, X, Y, and Z, each having the same diameter and height. Each cylinder had a hole at each of 5 depths, D, measured from the top of the cylinder. All of the holes in a given cylinder had the same cross-sectional area, A. Holes other than the one being tested were covered with tape.

In each trial, R and L were determined for one value of D. Throughout each trial, a student kept the cylinder being tested filled to the brim with water. Another student positioned a beaker to capture the stream of water. Using a stopwatch, the students measured the time, t, in seconds (sec), required for 100 cm³ of water to accumulate in the beaker. Using the formula R = 100 cm³ ÷ t sec, they calculated R in cm³/sec. Finally, using a tape measure, they found L in cm.

Study 1

Using Cylinder X, the students found R and L for each D. The cross-sectional area A of each hole in Cylinder X equaled 0.0100 cm² (see Table 1).

Study 2

Using Cylinder Y, the students found R and L for each D. The area A of each hole in Cylinder Y equaled 0.0200cm² (see Table 2).

Study 2

Using Cylinder Z, the students found R and L for each D. The area A of each hole in Cylinder Z equaled 0.0300 cm² (see Table 3).