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: 7b

Answer

The net work done on the water is positive in arrangement 2

Work Step by Step

Let $m$ be the mass of the unit volume of water. 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 unit volume of 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. In arrangement 2, the leftmost pipe radius is larger than the rightmost pipe radius. Thus the speed of the water is faster in the rightmost pipe than in the leftmost pipe. Then the kinetic energy of the water in the rightmost pipe is larger than the kinetic energy of the water in the leftmost pipe. Therefore, the net work done on the water is positive in arrangement 2
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