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beetleblur

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I'm currently investigating a simple experiment involving two different capacity syringes filled with water and then applying a constant force to see their maximum verticle squirting height; My basic apparatus is basically this;

We have a 10ml and a 2ml syringe and we drive them using a set of weights we had specifically made between 300-500g and we measure the maximum height using a high-speed camera set up, and compare both. I'm basically struggling with some of the concepts involved, despite being relatively simple (i think I've been overthinking everything)

My real issue is understanding the principles involved with the pressure's within the syringe. Using the volume flow continuity A1v1=A2v2 and bernoulli's equation in unison, I thought i'd get some mutual answers (i.e plugging known numbers to find v1 by bernoulli's) but bernoulli gave a result which didn't compare to the experimental result and applying the continuity. I

thought P1 = mg/A and P2 would be just atmospheric pressure as the fluid would be in the air, but is it really that simple? The height obviously increases as the force used to drive syringe onto the plunger increases meaning that the pressure increases, but what am I missing to describe the system accurately?

for example, using continuity laws, for 510g of mass on the 10ml syringe, the height was roughly 65cm, hence v2 = sqrt(2gh)= 3.57m/s

so if A1 is roughly =piR^2 = 3.14x10-4

and A2 is roughly = pir^2 = 3.14x10-6

so v1 = 0.0357m/s

Bernoulli's = P1+0.5ρv1^2+ρgh1=P2+0.5ρV2^2+ρgh2, but I understand that the pressure changes with time as the mass acts on the syringe. If i choose P1 as mg/A1 where mg is just the applied mass, P1=15.9kPa, P2= 101235 Pa, v2=3.57m/s and h1=0.11m (hence h2=0) gives v1 = 13.55m/s; an unphysical result; Is the pressure P1 something like (F/A)-Atmospheric?

Can anyone show me where I am going wrong? If there is any relevant theory and I'm treating the problem too simply then any hints would be great (Poiseuille flow etc..) but i suspect that it's something to do with how I'm thinking about the problem; I had initially tried a simple force diagram as v1 = speed syringe falls onto plunger..

thanks!