Pressure of fluid leaving a syringe

In summary, the conversation discusses finding an equation to determine the pressure of a fluid leaving a hypodermic needle, with only the diameter of the hole and flow rate known. Suggestions are given to use Bernoulli's equation or Poiseuille flow, and the person ultimately figures out the solution.
  • #1
nerdguy
2
0
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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  • #2
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.
 
  • #3
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.
 
  • #4
Thank you for the help. I think I figured it out. Science rocks!
 
  • #5


Hello,

Finding the pressure of a fluid as it leaves a syringe can be calculated using the Bernoulli's principle, which states that the total energy of a fluid remains constant as it flows through a system. In this case, the energy of the fluid at the syringe's exit point can be equated to the energy at the entrance of the IV line.

To calculate the pressure, you can use the following equation:

P1 + 1/2ρv1² + ρgh1 = P2 + 1/2ρv2² + ρgh2

Where P1 and P2 are the pressures at the entrance and exit points respectively, ρ is the density of the fluid, v1 and v2 are the velocities at the entrance and exit points, and h1 and h2 are the heights of the fluid at the entrance and exit points respectively.

To find the velocity at the exit point, you can use the equation for flow rate:

Q = Av

Where Q is the flow rate, A is the area of the hole, and v is the velocity at the exit point.

By rearranging the equations, you can solve for the pressure at the exit point, which will give you the pressure of the fluid leaving the syringe. Keep in mind that this calculation assumes an ideal fluid with no friction.

I hope this helps guide you in the right direction. If you have any further questions, please don't hesitate to ask. Best of luck with your research!
 

What is the pressure of fluid leaving a syringe?

The pressure of fluid leaving a syringe depends on several factors such as the volume of fluid, the size of the syringe, the force applied to the plunger, and the viscosity of the fluid. The pressure can range from a few pounds per square inch (psi) to several hundred psi.

How does the size of the syringe affect the pressure of fluid leaving?

The size of the syringe affects the pressure of fluid leaving because a larger syringe will require more force to push the same amount of fluid out compared to a smaller syringe. This means that the pressure will be higher in a smaller syringe compared to a larger syringe.

What is the relationship between volume of fluid and pressure?

The relationship between volume of fluid and pressure is directly proportional. This means that as the volume of fluid increases, the pressure also increases. This is because more force is needed to push a larger volume of fluid out of the syringe.

Does the viscosity of the fluid affect the pressure of fluid leaving?

Yes, the viscosity of the fluid can affect the pressure of fluid leaving a syringe. Viscosity is a measure of how thick or thin a fluid is. Thicker fluids, such as honey, will require more force to push out of a syringe compared to thinner fluids, such as water. This means that the pressure will be higher for thicker fluids.

How can the pressure of fluid leaving a syringe be measured?

The pressure of fluid leaving a syringe can be measured using a pressure gauge or a manometer. These devices can be attached to the syringe to measure the pressure of the fluid as it is being pushed out. Alternatively, the pressure can also be calculated by measuring the force applied to the plunger and the area of the syringe's opening.

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