Hello there Physics Forum! This is my first post here. This problem has been boggling me all day and I'm need of help in piecing together what I've come up with so far. I'm currently working on a personal project related to paint spraying. In this project I'm using a syringe & needle to feed the paint through a spraying nozzle that will atomise the paint. However, to record the results I retrieve (diameter/reach of spray for different needle diameters and plunger speeds), I'd like to know at what pressure the paint is at when leaving the syringe. The syringe will be depressed at a constant velocity of around 5mm/s or 0.005m/s. The area of the syringe and needle are 0.00055m2 and 2.01x10-6m2 respectively. From this I've worked out the velocity at the end of the needle using: v2 = v1 A1 / A2 = 1.372m/s and a flow rate out of the end of the needle by simply multiplying velocity by area to get 9.93 L/h. I have also used Bernoulli's to find the change in pressure between the syringe and the needle: ΔP = ½ ρ ( v12 - v22 ) ΔP = 12253 Pa (assuming density of water for now 1060kg/m3) However from here I'm a little stuck. To utilise the pressure change I'd first need to know the pressure in the syringe? This would have to be worked out using the force which is presumably some function of the velocity of the plunger and the viscosity of the liquid inside. Also, will the pressure change as the syringe is emptied? I'm not sure whether I'm over complicating or under complicating this problem. Please help! Note: I realise that once the liquid leaves the needle it's pressure will technically be atmospheric. I assume I'm looking for velocity pressure or something to that effect? Many thanks, Sean.