About once every 30 minutes, a geyser known as Old Faceful projects water 12.0 m

Question

About once every 30 minutes, a geyser known as Old Faceful projects water 12.0 m straight up into the air. Use g = 9.80 m/s, and take atmospheric pressure to be 101.3 kPa. The density of water is 1000 kg/m3 (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 5.00 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

Solution-
Using Bernoulli's equation-
it is
P1+0.5v1^2+gy1= P2+0.5v2^2+gy2
Now
P1=P2, v2=0 and y2-y1=h
v1=sqrt(2gh)
=sqrt(2*9.8*12)=15.34 m/s

b) P1= Patm+ g(17)
P1= (101.3*10^3+1000*9.8*17)
=267.9 KPa

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