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

[jerry wickey]

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.

 

[Buffu]

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.

 

[jerry wickey]

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

http://jerrywickey.com/emails/IMG_00010.JPG http://jerrywickey.com/emails/IMG_00011.JPG

 

[Nidum]

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 .

 

[jerry wickey]

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.

 

[Nidum]

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 ?

 

[jerry wickey]

it drains into ambient pressure water. The same pressure water from which the stream began with a pump