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

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Discussion Overview

The discussion revolves around the application of Bernoulli's principle to understand pressure changes in fluid dynamics, particularly in the context of a liquid simulator being developed by a participant. The focus includes the relationship between flow rate, velocity, and pressure in a system with varying pipe diameters.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant seeks to express pressures p1 and p2 in terms of flow rate (f), velocity (v), and radius (r), highlighting the conservation of flow rate and the implications of Bernoulli's principle on dynamic pressure.
  • There is confusion regarding how dynamic pressure translates into static pressures measured by "head" in pressure tubes, with a request for clarification on negative pressure changes indicated by Bernoulli's equations.
  • Another participant suggests initially omitting the vertical pressure gauge tubes to focus on solving the flow problem in the horizontal sections before addressing the pressure measurements.
  • A participant expresses difficulty in determining absolute or gauge pressure from the flow rate, noting that they can only find a negative pressure differential.
  • Questions arise about the conditions at the outlet of the smaller pipe, specifically whether the flow is draining freely into open air or into further equipment that could create back pressure.
  • It is clarified that the flow drains into ambient pressure water, which is the same source from which the pump initially draws water.

Areas of Agreement / Disagreement

Participants express various uncertainties regarding the calculations of pressures and the implications of Bernoulli's principle. There is no consensus on how to resolve the issues raised, and multiple competing views on the approach to the problem exist.

Contextual Notes

Participants mention difficulties with translating dynamic pressure into static pressure measurements and the implications of negative pressure values. The discussion does not resolve these mathematical steps or assumptions.

jerry wickey
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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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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.
 
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

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http://jerrywickey.com/emails/IMG_00010.JPG http://jerrywickey.com/emails/IMG_00011.JPG
 
Last edited by a moderator:
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 .
 
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.
 
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 ?
 
it drains into ambient pressure water. The same pressure water from which the stream began with a pump
 

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