Pressure of fluid leaving a syringe

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SUMMARY

The discussion centers on calculating the pressure of fluid exiting a hypodermic needle using the diameter of the hole and flow rate. The recommended approach is to utilize Poiseuille's law rather than Bernoulli's equation, as the latter is not applicable due to the viscous nature of the flow at this scale. Key factors influencing the pressure include the diameter of the plunger, the force applied, and the fluid's properties. Understanding these principles is essential for accurate pressure calculations in fluid dynamics.

PREREQUISITES
  • Understanding of Poiseuille's law for viscous flow
  • Knowledge of fluid properties such as viscosity and density
  • Familiarity with basic fluid dynamics concepts
  • Ability to apply mathematical equations related to pressure and flow rate
NEXT STEPS
  • Research Poiseuille's law and its applications in fluid dynamics
  • Learn about the properties of fluids, including viscosity and density
  • Study the effects of diameter and force on fluid pressure in syringes
  • Explore the limitations of Bernoulli's equation in real-world applications
USEFUL FOR

Engineers, medical professionals, and anyone involved in fluid mechanics or medical device design, particularly those working with syringes and IV lines.

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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