Question

About once every 30 minutes, a geyser known as Old Faceful projects water 16.0 m straight up into the air. Use

g = 9.80 m/s²,

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 6.00 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?

Answer 1

(a)

Applying Bernoulli's principle at the opening of crack and at the top of water jet

Since pressure at both points is same as atmospheric pressure,  

speed of water at the top of water jet is zero

Measuring the height of different points from ground level,

Speed of water at the opening of crack

(b)

Applying Bernoulli's principle at the opening of crack and inside the large chamber,

Since pressure at the opening of crack is same as atmospheric pressure,  

Using equation of continuity,

Since the opening of crack is narrow, and chamber is of large cross-sectional area.

and

Measuring the height of different points from ground level, and

Speed of water at the opening of crack

Since  ,  

Pressure in the chamber is