How can Bernoulli's principle help explain pressure changes in fluid dynamics?

In summary, Bernouli's equations state that the change in velocity requires a change in dynamic pressure to conserve the energy. However, I can't seem to figure out how dynamic pressure translates into the static pressures which are measured by the "head" which would be developed in both pressure measure tubes. I can't seem to translate the negative pressure changes given by Bernouli equations into dynamic and total pressures which would appear in the measure tubes. Tube on the left would have a higher water level than the tube on the right.
  • #1
jerry wickey
4
0
pressure.png

Can someone smarter than I, please express p1 and p2 in terms of f, or v and r?

The pump pushes out water at f rate which creates velocity v in the bigger pipe. When the water comes to the restriction velocity increases while flow rate is conserved. Bernouli tells us that the change in velocity requires a change in dynamic pressure to conserve the energy. However, I can't seem to figure out how dynamic pressure translates into the static pressures which are measured by the "head" which would be developed in both pressure measure tubes. I can't seem to translate the negative pressure changes given by Bernouli equations into dynamic and total pressures which would appear in the measure tubes. Tube on the left would have a higher water level than the tube on the right.

If someone can, please show me. I am a computer programmer writing a liquid simulator for my employer for a very specific application. Thank you so much for anyones help.
 
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  • #2
jerry wickey said:
pressure.png

Can someone smarter than I, please express p1 and p2 in terms of f, or v and r?

The pump pushes out water at f rate which creates velocity v in the bigger pipe. When the water comes to the restriction velocity increases while flow rate is conserved. Bernouli tells us that the change in velocity requires a change in dynamic pressure to conserve the energy. However, I can't seem to figure out how dynamic pressure translates into the static pressures which are measured by the "head" which would be developed in both pressure measure tubes. I can't seem to translate the negative pressure changes given by Bernouli equations into dynamic and total pressures which would appear in the measure tubes. Tube on the left would have a higher water level than the tube on the right.

If someone can, please show me. I am a computer programmer writing a liquid simulator for my employer for a very specific application. Thank you so much for anyones help.

Question like this will be closed if you do not show your work.
 
  • #3
Dear https://www.physicsforums.com/threads/fluid-dynamics-bernoulli.902341/members/buffu.606620/ ,

I'm not sure what adversity you feel you are protecting the forum from, but I worked on this problem all work day. I must be missing something stupid and simple, but I can't find it and I hope someone knows what I am missing. I attached pics of all my work today

IMG_0005.JPG
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http://jerrywickey.com/emails/IMG_00010.JPG http://jerrywickey.com/emails/IMG_00011.JPG
 
Last edited by a moderator:
  • #4
The two vertical tubes are really just pressure gauges . Omit them initially and solve the primary problem of flow in the two horizontal pipe sections . When you've done that you can go back and find the column heights in the vertical tubes which will balance the calculated pressures in the horizontal pipe sections .
 
  • #5
Yes they are, but I don't know how to solve for pressure absolute or gauge given flow rate. I can find only the the pressure differential which is a negative value. I need to know the gauge pressure. i.e. How high will the pressure push the water in the vertical tubes.
 
  • #6
What are conditions at the final outlet of small pipe ? Is the flow just draining freely into the open air or is continuing into further equipment which could generate a back pressure ?
 
  • #7
it drains into ambient pressure water. The same pressure water from which the stream began with a pump
 

FAQ: How can Bernoulli's principle help explain pressure changes in fluid dynamics?

What is Fluid Dynamics Bernoulli?

Fluid Dynamics Bernoulli is a branch of physics that studies the behavior of fluids, which includes liquids and gases, in motion. It specifically focuses on the relationship between pressure, velocity, and height in a fluid flow.

Who is Bernoulli and why is he important in Fluid Dynamics?

Daniel Bernoulli was a Swiss mathematician who discovered the principle of conservation of energy in fluid flow, now known as Bernoulli's principle. This principle is important in Fluid Dynamics as it explains the relationship between fluid velocity and pressure, and is used in various applications such as aerodynamics and hydraulics.

What is the Bernoulli equation and how is it used?

The Bernoulli equation is a mathematical expression that relates the pressure, velocity, and height of a fluid at any point in a flow. It is used to calculate the change in any of these properties in a fluid flow, and is especially useful in analyzing flow through pipes, nozzles, and wings.

What are some real-life applications of Fluid Dynamics Bernoulli?

Fluid Dynamics Bernoulli has various real-life applications, including in the design of aircraft wings, ventilation systems, and water turbines. It is also used in weather forecasting, oceanography, and the study of blood flow in the human body.

Are there any limitations to the Bernoulli principle?

While the Bernoulli principle is a useful tool in Fluid Dynamics, it does have some limitations. It assumes that the fluid is incompressible, non-viscous, and flows in a steady state. In reality, these assumptions may not always hold true, and therefore the results obtained from the Bernoulli equation may not be completely accurate.

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