Old Faithful geyser in Yellowstone Park erupts at approximately 1-hour intervals

Question

Old Faithful geyser in Yellowstone Park erupts at approximately 1-hour intervals, and the height of the fountain reaches 42.0 m. 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. _____ m/s 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. ____ m/s What is the pressure (above atmospheric pressure) in the heated underground chamber 174 m below the vent? You may assume the chamber is large compared with the geyser vent. ____ MPa

Explanation / Answer

1.

use from gravitational effects offree fall body

h = u^2/2g

u^2 = 2 g h

u^2 = 2* 9.81 * 42

u = 28.7 m/s

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b.

use rho gh = 0.5 rgo v^2

v = 28.7 m/s

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c.

given that,

density of water = water =1000

reqiured presuure = P-P0 = rho * 9.81 * (h+174)

P- Po = 1000 * 9.8*(42 +175)

P-P0 = 2.12 * 10^6 Pa or = 2.12 Mpa

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