Why Does Water Flow at Lower Pressure Than Atmospheric Pressure?

[Idea04]

Homework Statement

I know with flowing water the amount of flow depends on the water pressure and atmospheric pressure surrounding that water.
So I'm wounding why, when water from a cityline is 15psi that rises up the house let's say 12 feet to the sink it will lose a certain amount of pressure, So when it leaves the taps on the sink it would have over 9 psi.
Why does the water flow when the atmospheric pressure is a higher value than the city water.

Homework Equations

The Attempt at a Solution

 

[turdferguson]

Do you know the Bernouli equation? It states that when the velocity is higher, the pressure is lower. It also says that the pressure is lower when the potential energy is higher:
P1 + .5pv1^2 + mgh1 = P2 + .5pv2^2 + mgh2

 

[Idea04]

So would that mean that if you have a container of water 12 feet in the air, the water has a lower pressure than the same amount of water on the ground. Even if its open to the atmosphere.

 

[Mentz114]

If the water is being pumped at a pressure of 14.7psi, it actually means 14.7psi + atmospheric pressure. All the water feels the atmosphere all around it so it cancels out. The rise of 9 ft is about 9/34 atmospheres which leaves about 10psi of the 14.7.