Abstract
In my article (Featonby 2015 Phys. Educ. 50 123), three holes were drilled in a large bottle of water, but which hole had the greatest range of water?
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The question asked which of three holes at heights of h/4, h/2 and 3h/4 from the bottom of the bottle will emit water with the greatest range [1]?
The range depends on the exit speed and the time taken for the water to reach the ground. The middle hole has the greatest range because v increases with water depth (i.e. water pressure), whilst t (the time taken for the water in the jet to reach the lower surface) decreases with water depth, so their product is greatest at the halfway point. This is shown in the photograph of figure 1. A rigorous derivation using calculus will show that the range for the middle hole is h, whilst the other two holes will have an identical range of 0.866h, 13% less than the middle hole. This is shown in the photograph.
Figure 1. Photograph showing that the jet with the greatest range is the middle one.
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Of course if the height of water in the column falls below h, then the calculation will change. A simple description is given by Ehrlich [2], whilst a more rigorous approach is given by Kireš [3].
Biographies
David Featonby 'retired' from school physics teaching after 35 years in the classroom, and until 2011 was a Teacher Network Coordinator. He has represented the UK at Science on Stage and now works voluntarily with the International Science on Stage (Europe) Committee as UK representative and member of its European Executive Board. David is the author of various hands-on articles in Physics Education and Science in School and has led workshops at many conferences throughout the UK and Europe. He is particularly interested in showing the physics in everyday things to the public, whatever their age.