Question about hydraulic jump assumptions

In summary, the conversation discusses the calculation of forces involved in a hydraulic jump. The person apologizes for a poor image and provides a link to a better picture. They also mention not understanding an assumption in the red box and explain their calculations for the forces, including the inclusion of atmospheric pressure. They also share a Wikipedia link for more information on hydraulic jumps. Ultimately, the conversation ends with the conclusion that only the gradient of pressure produces a force on the region and that the pressure on the jump area must be taken into account for accurate calculations.
  • #1
Clara Chung
304
14
96.png

Sorry for the poor image... A better picture can be viewed here https://www.dropbox.com/s/uyi01l27vu2fwyw/96.png?dl=0
I don't understand the assumption in the red box...
If I don't ignore the atmospheric pressure, F_1 = integrate from 0 to h_1 (ρg(h_1-z)+p_a)dz = 1/2 ρgh_1^2 + p_a*h_1, similarly for F_2.. Therefore, the final line would be f_3(h) = h^2 + 2Q^2/gh +2/ρg*p_a*h which a linear term is added...
 
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  • #3
Thanks for the reference links.
 
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  • #4
I think I got the answer...
Only the gradient of pressure produce a force on the region. (The euler equation)
If I really want to included the atmospheric pressure as well, I also have to account for the pressure on the acting on the jump area... Therefore, p_a*h_1 + p_a*(h_2-h_1) balances the force on the other side p_a*h_2...
 
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Related to Question about hydraulic jump assumptions

1. What is a hydraulic jump?

A hydraulic jump is a phenomenon that occurs when a fast-moving, shallow stream of fluid suddenly slows down and becomes deeper. This results in a turbulent mixing of the fluid and a sudden increase in energy loss.

2. What are the assumptions made in the analysis of hydraulic jumps?

The most common assumptions made in the analysis of hydraulic jumps include the conservation of mass, energy, and momentum, as well as the neglect of frictional and viscous effects.

3. Why are these assumptions necessary?

These assumptions are necessary because they simplify the equations and make it easier to analyze the hydraulic jump phenomenon. They also provide a good approximation of the real-world scenario in most cases.

4. Are there any situations where these assumptions may not be valid?

Yes, in some cases, these assumptions may not be valid. For example, in situations where there is a significant amount of friction or viscosity present, or when the fluid is highly compressible, these assumptions may not accurately represent the behavior of the hydraulic jump.

5. How do these assumptions affect the accuracy of the analysis?

The accuracy of the analysis is affected by these assumptions to some extent. While they may not accurately represent the real-world scenario in certain situations, they provide a good approximation and allow for a simpler analysis of the hydraulic jump phenomenon.

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