Question about hydraulic jump assumptions

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Discussion Overview

The discussion revolves around the assumptions made in analyzing hydraulic jumps, particularly concerning the treatment of atmospheric pressure in the force calculations. Participants explore the implications of including atmospheric pressure in their equations and how it affects the overall analysis.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant questions the assumption regarding atmospheric pressure in the force calculations, suggesting that ignoring it leads to an incomplete understanding of the forces involved.
  • Another participant provides a reference to a Wikipedia article on hydraulic jumps, indicating their unfamiliarity with the topic and seeking additional context.
  • A different participant proposes that only the gradient of pressure contributes to the force in the region, referencing the Euler equation, and suggests that including atmospheric pressure requires additional considerations regarding the pressure acting on the jump area.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the treatment of atmospheric pressure, with differing views on its relevance and the implications for the analysis of hydraulic jumps.

Contextual Notes

Limitations include potential missing assumptions about the system being analyzed and the dependence on specific definitions of pressure in the context of hydraulic jumps.

Clara Chung
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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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Thanks for the reference links.
 
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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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