Why does atmospheric pressure cancel in hydraulic jump analysis?

[Clara Chung]

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...

 

[Charles Link]

Try this: https://en.wikipedia.org/wiki/Hydraulic_jump The topic is totally new to me.

 

[swara31]

Thanks for the reference links.

 

[Clara Chung]

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...