Chapter 9, Problem 47P

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

# Old Faithful geyser in Yellowstone Park erupts at approximately 1-hour intervals, and the height of the fountain reaches 40.0 m (Fig. P9.47). (a) Consider the rising stream as a series of separate drops. Analyze the free-fall motion of one of the drops to determine the speed at which the water leaves the ground. (b) Treat the rising stream as an ideal fluid in streamline flow. Use Bernoulli’s equation to determine the speed of the water as it leaves ground level. (c) What is the pressure (above atmospheric pressure) in the heated underground chamber 175 m below the vent? You may assume the chamber is large compared with the geyser vent.

(a)

To determine
The speed at which the water leaves the ground.

Explanation
When one of the drop reaches the maximum height, its speed would be vy2=0=v0y2+2ay(Î”y)â‡’v0y=âˆ’2ay(Î”y) .

Given info: The deceleration of the water drop is âˆ’9.80â€‰m/s2 and the height of the fountain is 40.0â€‰m

(b)

To determine
The speed of the speed of the water as it leaves ground level.

(c)

To determine
The pressure in the heated underground chamber 175 m below the vent.

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