Demos: 2B-07 Liquid Stream Trajectories

A tall cylinder has three holes drilled such that when the cylinder is filled, the central hole is half the height of the liquid. The other holes are equidistant from top and bottom. When the holes are opened, pressure drives water out the holes horizontally so that each stream becomes a horizontal projectile. It is observed that the maximum range occurs in the stream that exits at the center.

According to Torricelli’s 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 can’t 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.

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