I'm a physics noob with a question that will probably stump nobody in this forum, but which Google can't seem to answer straightforwardly for me.

Here it is: I want to build three hot tubs which will all be connected via two 2-inch tubes at the bottom. The tubs will all be the same height, and situated level with one another. Two will have 150 gallons of water, one will have 300 gallons of water.

Will the additional volume in the 300 gallon tank equate to more pressure at the 2-inch tubes, such that the water level might not be the same across all three tanks? Put another way, if I sit in one of the 150 gallon tanks, will the water I displace move to the adjacent 300 gallon tank?

  • $\begingroup$ Are you asking whether the water level in all three tanks will be the same when you sit in one of the 150 gallons tanks? $\endgroup$ – Chet Miller Nov 4 '17 at 12:10
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    $\begingroup$ When you connect the tanks with big tubes at the bottom, you are making it effectively one big tank. So if you lower yourself into one part of it, raising the water there, water will flow out of that part into the other parts until the water is level throughout. $\endgroup$ – Mike Dunlavey Nov 4 '17 at 13:23
  • $\begingroup$ This post (v2) sounds more like an engineering than a physics project. $\endgroup$ – Qmechanic Nov 4 '17 at 18:48
  • $\begingroup$ Yes Chester, and thanks Mike! That's what I presumed, but I thought the additional volume in the 300 gallon tank might create more outward pressure at the connecting tubes, and thus impede the flow of water from the smaller tanks to the larger one. $\endgroup$ – rs695 Nov 4 '17 at 19:19

Firstly, you need to know that fluid pressure at a point in a liquid, $P = h \rho g$, where $h$ is the height of liquid column above that point, and $\rho$ is the density of the liquid.

Also, if three different vessels containing the same liquid connected, then the level of liquid in the three vessels is same, irrespective of the size or shape of the vessels.

Now, in your case, if the size and shape of the three tanks are same, and if they are connected, then there can be no way in which the level of liquid is different in the three tanks. If, however, you control the flow of liquid in the pipe, then the height of liquid in the 300 gallon tank will be higher than the others, and that will amount to more pressure on the pipe at the bottom, as per the equation I've stated previously.

If you lower yourself in one tank, and the liquid is allowed to flow freely in the pipes, then at first, the water in the tank in which you're lowering yourself, will rise, but then water will flow though the pipes such that the liquid level is the sane throughout in the tanks. But keep in mind that the upthrust will still act upon you.

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  • $\begingroup$ @rs695 Welcome. If the answer suits you, you can also accept it, just to indicate that the question has been answered. $\endgroup$ – Wrichik Basu Nov 4 '17 at 19:25

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