Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 14 - Fluids - Questions - Page 406: 9

Answer

We can rank the three lettered sections of the pipe according to the pipe radius: $B \gt C \gt A$

Work Step by Step

Let $m$ be the mass of the water element. We can write an expression for the kinetic energy of the water: $K = \frac{1}{2}mv^2$ Since the mass does not change as the water flows through pipes of differing radii, the kinetic energy of the water depends on the speed. We know that the water flows faster when the pipe radius is smaller, and the water flows slower when the pipe radius is larger. That is, the kinetic energy is greater when the pipe radius is smaller, and the kinetic energy is smaller when the pipe radius is larger. We can rank the three lettered sections of the pipe according to the pipe radius: $B \gt C \gt A$
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