Question about hydraulic jump assumptions

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The discussion centers on the assumptions related to hydraulic jumps, particularly the role of atmospheric pressure in force calculations. The user expresses confusion about the assumption depicted in a referenced image and explores the integration of pressure terms in their calculations. They conclude that only the pressure gradient contributes to the force in the hydraulic jump region, as described by the Euler equation. Additionally, they clarify that including atmospheric pressure requires balancing forces on both sides of the jump area. The conversation highlights the complexities of hydraulic jump analysis for those new to the topic.
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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