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Think It Over

This section of Resonance presents thought-provoking questions, and discusses answers a few months later. Readers are invited to send new questions, solutions to old ones and comments, to ‘Think It Over’, Resonance, Indian Academy of Sciences, Bangalore 560 080. Items illustrating ideas and concepts will generally be chosen.

A Maze Problem

There are many stories about people getting lost inside complicated mazes. One way to avoid getting lost is to always touch the left wall (or always touch the right wall) as you grope your way. Then you are sure to find your way back to the entrance. This is obvious since you will always move in a loop which comes back to the starting point. But the trouble is that this will not ensure that you have visited the entire maze, as in Figure 1.

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Address for Correspondence

Arnab Chakraborty
Department of Statistics
Stanford University
California, USA

Squeeze for Speed

J H Arakeri

While watering our garden with water coming out of a flexible pipe we often press the end of the pipe to get a higher velocity of the water (see Figure). An application of Bernoullis’ equation shows that in both cases a and b in Figure, the velocity of the water coming out of the pipe is

SqRoot(2gH)

where H is the height of the water level in the tank above the pipe exit.

Then, how can we explain that a reduction of the exit area increases the velocity of the water coming out? Is there a difference in the two flow rates?

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Address for Correspondence

J H Arakeri
Department of Mechanical
Engineering
Indian Institute of Science
Bangalore 560 012, India.

Indian Academy of Sciences
C.V.Raman Avenue, Post Box No. 8005,
Sadashivanagar Post, Bangalore 560 080