Pressure of fluid leaving a syringe

[nerdguy]

I am trying to find an equation to find the pressure of a fluid as it leaves a hypodermic needle when all I have is the diameter of the hole the fluid is discharging from and the flow rate. Can anyone point me in the right direction? I think this should be simple but I have spent a couple of hours trying figure this out. I would like to find out what the pressure would be going into say an IV line of the same dimension as the hole of the syringe if that makes sense. I appreciate any ideas. Thanks for your time.

 

[russ_watters]

Welcome to PF!

You're looking for Bernoulli's equation: http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html

You do need more than just the diameter of the hole though, of course. Like the diameter of the plunger and the force applied by the person pushing it and the properties of the fluid.

 

[boneh3ad]

Using Bernoulli's principle here is a bad idea. Bernoulli only holds for inviscid flow and at these scales, the flow isn't even close to being approximately inviscid. Look up Poiseuille flow. That ought to get you started.

 

[nerdguy]

Thank you for the help. I think I figured it out. Science rocks!