Question about hydraulic jump assumptions

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SUMMARY

The discussion centers on the assumptions related to hydraulic jumps, specifically the treatment of atmospheric pressure in force calculations. The user integrates pressure terms to derive forces F_1 and F_2, concluding that atmospheric pressure must be accounted for in the force balance across the jump. The final expression for force includes terms for both the pressure gradient and atmospheric pressure, confirming that only the gradient of pressure produces a force in the region, as described by the Euler equation. The user references the Wikipedia page on hydraulic jumps for further clarification.

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Clara Chung
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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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