Pressure of fluid leaving a syringe

AI Thread Summary
To determine the pressure of fluid exiting a hypodermic needle, it's essential to consider factors beyond just the hole's diameter and flow rate. Bernoulli's equation is not suitable due to the non-inviscid nature of the flow at this scale. Instead, Poiseuille's law should be referenced for a more accurate analysis. Additional variables such as the diameter of the plunger and the force applied are also crucial for calculating the pressure accurately. Understanding these principles can lead to a clearer solution for the pressure in an IV line.
nerdguy
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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.
 
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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.
 
Thank you for the help. I think I figured it out. Science rocks!
 

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