To figure out how fast the water is moving when it comes out of the ground, we could simply use conservation of energy, and set the potential energy of the water 25 m high equal to the kinetic energy the water has when it comes out of the ground. Another way to do it is to apply Bernoulli's equation, which amounts to the same thing as conservation of energy. Let's do it that way, just to convince ourselves that the methods are the same.

Bernoulli's equation says:

But the pressure at the two points is the same; it's atmospheric pressure at both places. We can measure the potential energy from ground level, so the potential energy term goes away on the left side, and the kinetic energy term is zero on the right hand side. This reduces the equation to:

The density cancels out, leaving:

This is the same equation we would have found if we'd done it using the chapter 6 conservation of energy method, and canceled out the mass. Solving for velocity gives v = 22.1 m/s.

To determine the pressure 35 m below ground, which forces the water up, apply Bernoulli's equation, with point 1 being 35 m below ground, and point 2 being either at ground level, or 25 m above ground. Let's take point 2 to be 25 m above ground, which is 60 m above the chamber where the pressurized water is.

We can take the velocity to be zero at both points (the acceleration occurs as the water rises up to ground level, coming from the difference between the chamber pressure and atmospheric pressure). The pressure on the right-hand side is atmospheric pressure, and if we measure heights from the level of the chamber, the height on the left side is zero, and on the right side is 60 m. This gives:

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