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If I were to move the syringe up, and cause it to be stationary, how does that effect the pressure at the bottom of the pipe? How does the movement of this water effect the system setup and pressure?

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I'm not seeing a syringe, do you mean a stopper, i.e., an object like a cork in a wine bottle that closes off the entire diameter of a vessel or conduit? –  Eugene Seidel Jan 13 '13 at 12:04
no a syringe - a stopper ...that can move... –  Hapjake Jan 13 '13 at 23:05

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Since it is closed at the bottom, the pressure felt at the bottom of the pipe is a function solely of the weight of the column above it. So this is the combined effect of the depth of the water column and the depth of the air column above.

So, if you move the syringe up, it will displace the water from the spigot area into the main pipe, making the water column deeper. So pressure at the bottom will increase.

Conversely, if you move the syringe down, more room is available in the spigot and the water column gets smaller. So pressure decreases.

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I understand that the pressure increases for the main pipe ..what kind of difference does it make on the syringe and spigot area? is the pressure divided between that area and the rest of the pipe? –  Hapjake Jan 13 '13 at 5:59
+ @Hapjake: Amount (volume) of water can be divided, but not pressure. Pressure depends purely on the height of water above the point at which the pressure is measured. An easy way to think of it is, suppose you have a tube with cross section 1 square cm, and you insert it into the water. Then the pressure at the bottom is just the weight of the water above the bottom (in the tube). –  Mike Dunlavey Jan 14 '13 at 16:15

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