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Feynman in his Feynman's lectures on physics, volume II, section 40-3, explains that, considering a tank with a re-entrant hole near the bottom, it is possible to prove "in a most beautiful way" that the area of the stream of water exiting will contract to 50% the area of the hole, without giving the actual proof.

He explains that this can be proven considering conservation of momentum, he then talks about the pressure near the walls of the tanks. In particular, he states that as the hole is re-entrant, the velocity of the fluid near the walls is negligible, thus the pressure near the walls can be calculated as the one of a fluid at rest.

Then he goes on saying that "the static pressure at any point on the side of the tank must be matched by an equal pressure at the point on the opposite wall, except at the points on the wall opposite the charge tube", and here I'm lost. If I understand well, he means that there is some kind of pressure gradient going from the side opposite to the hole and the hole itself, but I don't see how this implies some use of momentum or its conservation or the shape of the stream after it has exited the hole.

Can someone help? If not by giving the proof, at least by clarifying what Feynman is saying here?

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  • $\begingroup$ Hi Chris, personally I love paragraphs for clarity, so I stuck some in. The Lectures are online, so I put a link to that as well. The best of luck with your question. My question is, where did Feynman find the time to write in such detail about almost every aspect of physics? $\endgroup$ – user108787 Dec 1 '16 at 18:00
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Perhaps the exposition by Kirk McDonald is helpful. You can also google "Vena Contracta" to find other sources.

P.S.: I admit that I'm not entirely sure what Feynman is saying in the quote you provide. The way it reads it doesn't even sound correct, but given the source that's probably a misunderstanding of mine.

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  • $\begingroup$ Thank you, that was helpful, I still do not understand what wall he's talking about when he writes "the wall of area A1-A2" $\endgroup$ – user2723984 Dec 1 '16 at 18:15
  • $\begingroup$ I cannot find the exact quote you gave above in the online version of his lectures. If he is talking about pressure on vertical sides, I could understand if he was talking about the side with the tube, where indeed the pressure is equal to the static pressure everywhere, except for the opening itself. However, the online version of the lecture clearly talks about the "points on the wall opposite the charge tube". The pressures there are equal to the hydrostatic pressure so this doesn't sound right to me. $\endgroup$ – Pirx Dec 1 '16 at 18:24
  • $\begingroup$ Ahh, I think I get it now: Feynman says that the pressures at opposite sides of the tank match everywhere, except at the location of the opening: There the pressure on the wall opposing the opening remains the same, but across the opening itself it is different (and lower), an the difference in pressure between these two sides is what drives the jet, which is the momentum balance argument. $\endgroup$ – Pirx Dec 1 '16 at 18:33

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