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fluidistic
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Homework Statement
A closed tank contains a liquid of density [tex]\rho[/tex] and a gas (over the liquid) at a pressure [tex]P[/tex]. Suppose there's a little hole (much smaller than the cross section of the tank so that when the liquid flows by the hole, the height of the liquid doesn't change with time) in the tank at a distance [tex]H[/tex] under the liquid' surface. Now suppose I plug a small tube (at the orifice) forming an angle [tex]\alpha[/tex] over the horizontal. How high will the liquid goes over the orifice, in terms of [tex]H[/tex] and [tex]\alpha[/tex]?
Homework Equations
None given.
The Attempt at a Solution
I've calculated the velocity of which the liquid leaves the tank : [tex]v=\sqrt{2 \left [ \frac{(P-P_{\text{atm}})}{\rho}+gH \right ] }[/tex].
Now how do I continue? I've tried something with conservation of energy but I'm sure I made an error since I get [tex]x=\frac{P-P_{\text{atm}}}{\rho g}+H[/tex] which doesn't depend on [tex]\alpha[/tex] as requested. I also notice that the height cannot be larger than [tex]H[/tex]! So my result is wrong.
I'd like to have some guidance, like "Consider a small element [tex]dr[/tex] and check out its velocity" or so.
Thanks.