Gauge pressure of water in a syringe needle

[LBRRIT2390]

College Physics

Homework Statement

The figure shows a syringe with a 4.0-cm-long needle, filled with water at 20celsius.
What is the gauge pressure of the water at the point P, where the needle meets the wider chamber of the syringe?

http://session.masteringphysics.com/problemAsset/1014207/7/jfk.Figure.P13.38.jpg

Homework Equations

Bernoulli's Equation

The Attempt at a Solution

I haven't even reached a solution yet because I am totally lost...
I just need some guidance/help working through the problem.

 

[LBRRIT2390]

The answer is 3200 Pa.

However, I do not know how to arrive at that solution. I'd reallllyyyyy appreciate it if someone could walk me through it, step by step.

 

[ideasrule]

Use Bernoulli's principle. Apply it to the two points where you have the most information: just outside the narrow tube, and very near the piston. You can figure out the speed of the piston from the volume continuity equation.