Demos: 2B-07 Liquid Stream Trajectories
According to Torricellis theorem, the speed with which the liquid exits the hole is given by
where h is the depth below the surface of the liquid. The time for the water to fall to the surface is
which gives for the range
This shows that there are two positions (interchange h and H - h) that give the same range and also that the range is maximized when h = H - h, or h = H/2.
Directions: Set the apparatus near the sink on the lecture desk so that the streams will land in the sink. The holes are taped over at first so that the cylinder can be filled. Remove the tapes and try to keep the container filled with water by pouring from a beaker. Even if you cant get the top and bottom streams to coincide, it will be evident that the middle stream has the greatest range.
Suggestions for Presentation: After telling the students that water will emerge from the three holes, have them guess what the ranges will be. Few will likely guess correctly. Have them think back on the projectile motion concepts, where horizontal speed and time of flight combined to give two angles for the same range and a maximum at the center angle, 45°. What we have here is also a combination of horizontal speeds and times of flight that yield similar results.