About once every 30 minutes, a geyser known as Old Faceful projects water 17.0 m

Question

About once every 30 minutes, a geyser known as Old Faceful projects water 17.0 m straight up into the air. Use g = 9.80 m/s^2, and take atmospheric pressure to be 101.3 kPa. The density of water is 1000 kg/m^3. (a) What is the speed of the water when it emerges from the ground? m/s (b) Assuming the water travels to the surface through a narrow crack that extends 7.00 m below the surface, and that the water comes from a chamber with a large cross-sectional area, what is the pressure in the chamber? kPa

Explanation / Answer

Part A :

apply gauge pressure P2 -P1 = 0.5 rho v^2 = rho gh

0.5 rho v^2 = (1000* 9.8 * 17)

0.5 rho v^2 = 166600

v^2 = 166600* 2/1000

V = 18.25 m/s

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P2-P1 = 0.5 rho V^2 + rho gh

P2-P1 = 0.5* 1000* 18.25^2 + 1000*9.8* 7

P2 = 101300 + 235131.25

P2 = 336.43 k Pa

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