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cvoss_1228

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I have a tiny horizontal syringe (no gravity effect). Initially the plunger is fully pushed in, such that there is no air or liquid in the barrel, and liquid (water) fills the needle that is attached to the barrel. The needle has one end connected to water at atmospheric pressure. The needle is 2.5 mm long with a diameter of 0.25 mm. The barrel area is 5 mm^2. From this starting position the barrel is pulled out with a 40N constant force. There is 5N of friction opposing plunger motion. We can assume the plunger is zero mass.

The questions I need help answering are:

1. What is the solution for velocity of the plunger as a function of time?

2. What is the solution for flow rate through the needle as a function of time?

3. Is there a maximum flow rate and/or acceleration, and if so how is this calculated?