Again, I appreciate the time you're taking to go through this with me!

Many thanks!

J

I have had a rethink about this problem an now think that I made it a bit overcomplicated with my equation of motion (which is correct but not needed)

My apologies.

As I understand the system, the plunger is pushed by the spring, which must therefore be precompressed so that it can push the plungers as it expands towards its equilibrium postion.

As the spring expands it exerts a diminishing force on the plunger, causing a reducing pressure on the fluid in the barrel of the syringe.

The fluid is thus forced out through the nozzle under a reducing pressure regime so exits at a continually reducing rate.

Under these circumstances an appropriate question is not how much fluid is discharged in a given time, but how much time is taken to discharge a given (presumably prescribed) amount of fluid.

Calculating this involves integrating the Torricelli equation I mentioned earlier, over time and under reducing head conditions.

If you are happy with this description I will post a sketch and some mathematics tomorrow.