What is the velocity of medicine emerging from a hypodermic syringe?

[rawimpact]

1. A hypodermic syringe contains a medicine with a density of water. The barrel of the syringe has a cross-sectional area of 2.5x10e-5 m^2. A force of 2N is exerted on the pluger (left, larger side). Determine the velocity of the medicine as it emerges from the needle

_________
\
\
(1) (2)=====
/
_________/

2. P1 + 1/2pV1^2 + pghi = P2 + 1/2pV2^2 + pghf

Area = 2.5x10e-5 m^s, Force = 2 N

P1 = F/A = 80,000 Pascals

Because Area decreases, Velocity increases decreasing pressure so we assume P2 = 0, is this correct why we make P2 = 0?

 

[rl.bhat]

Inside the syringe pressure in the liquid is sum of atmospheric pressure and pressure due 2N force. Outside the syringe there is only atmospheric pressure.