How can I calculate h from this diagram

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Discussion Overview

The discussion revolves around calculating the height (h) of a manometer reading in a fluid dynamics scenario involving water flow in a horizontal pipe and mercury in a manometer. Participants explore the application of Bernoulli's equation and the relationship between pressure differences and fluid height.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant calculates the speed of water at point B using the continuity equation (A1V1 = A2V2) and applies Bernoulli's equation to find a pressure difference.
  • Another participant suggests that assuming a cross-sectional area for the mercury tubing could help in balancing forces at the mercury surfaces, emphasizing the need for equilibrium.
  • Several participants request further elaboration on the steps following the application of pressure differences and the implications of fluid height changes in the context of the manometer.
  • One participant notes that applying Bernoulli's equation again for the mercury in the U-tube could be beneficial, indicating that the area of the tube sides is not necessary for the calculation.

Areas of Agreement / Disagreement

Participants express a mix of agreement on the need to apply Bernoulli's equation and the importance of pressure differences, but there is no consensus on the next steps or the specific calculations required to determine h.

Contextual Notes

Participants have not fully resolved the assumptions regarding pressure differences and the specific conditions under which the calculations are made. There are also unresolved questions about the implications of fluid height changes.

Furious
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Member warned about not using the homework template
aNbzApR.jpg

Water flows in the horizontal pipe shown in Fig. 13-6. At A the area is
f1064g1q1g1.gif
and the speed of the water is
f1064g1q1g2.gif
At B the area is 16.0 cm2. The fluid in the manometer is mercury, which has a density of
f1064g1q1g3.gif
What is the manometer reading h?

My attempt:
I used A1V1 = A2V2 to find the speed at B which is 3.125
Then I used Bernoulli equation and I have: P(A) = P(B) + 2883
 
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In future, please retain and use the formatting template provided when you start a thread in the homework areas.

Assuming that you have the correct pressure difference between A and B then if you assume some cross-sectional area for the mercury tubing you should be able to assign forces at the mercury surfaces. Since the mercury is in equilibrium, something needs to balance out the forces applied at the surfaces...
 
Last edited:
gneill said:
In future, please retain and use the formatting template provided when you start a thread in the homework areas.
Noted and addressed.
 
Last edited:
gneill said:
In future, please retain and use the formatting template provided when you start a thread in the homework areas.

Assuming that you have the correct pressure difference between A and B then if you assume some cross-sectional area for the mercury tubing you should be able to assign forces at the mercury surfaces. Since the mercury is in equilibrium, something needs to balance out the forces applied at the surfaces...
hey, can you please elaborate.
p(a) is applied on left side and on right side p (a) - 2883 but what is the next step?
 
Furious said:
hey, can you please elaborate.
p(a) is applied on left side and on right side p (a) - 2883 but what is the next step?
What might cause a change in pressure with height (or depth) in a fluid?
 
Furious said:
hey, can you please elaborate.
p(a) is applied on left side and on right side p (a) - 2883 but what is the next step?
Furious said:
hey, can you please elaborate.
p(a) is applied on left side and on right side p (a) - 2883 but what is the next step?
You know p1 - p2. Just apply Bernoulli again for the mercury in the U-tube. (You don't need to know the area of either side of the tube; in fact, they can be very different.)
 
Last edited:

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