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

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jerry wickey
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Hand-drawn schematic of a pipe with a pump on the left feeding a wide section that narrows to a smaller outlet, with two vertical manometer tubes labelled p1 and p2 and radius and flow labels.

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:
Hand-drawn schematic of a pipe with a pump on the left feeding a main pipe that branches into two vertical standpipes marked p1 and p2, with a narrower outlet pipe on the right; labels give radius r, area pi*r^2, flow rate f cm^3/s, velocity v = f / r^2/pi cm/s, r2 = 1/3*r, and v2 = v / r2^2 * r^2.

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

Handwritten notes on lined paper: a pipe diagram with inlet V1, A1, F1 and outlet H1, H0, Vo, Ao, Fo; definitions of area, flow, head and velocity; flow equations F1 = Fo and V1·A1 = Vo·Ao; unit conversions and a density note of 1024 kg/m3.
Handwritten notes on lined paper showing a fluid dynamics calculation with a sketch of a pipe or nozzle labelled A1 and A2, and equations relating area, velocity and density.
Blurry photo of handwritten pencil work on lined paper, mostly illegible, including a short heading and a few equation fragments near the top left.
Handwritten work on lined paper rotated sideways: F0 = F1 = V1·A1 = A1·V1, with 'density ... of Sea water' as 1024 kg/m^3, 6.3927 lb/ft^3, and a result of 63.9279 lb/ft^3 followed by a series of equations for V0 and V1/V2.
Handwritten working on lined paper: F/A = K·Δx² with K = 2.02 N and a series of substitutions, ending with F = (K = 101.3 N/m)·(Δx²) and F = 7.48 g/m with Δx² = 7.481 cm².
http://jerrywickey.com/emails/IMG_00010.JPG http://jerrywickey.com/emails/IMG_00011.JPG
 
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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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