B Discovering the Mystery Behind the Direction of Water Swirl in Your Sink

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The direction of water swirl in sinks is influenced more by initial conditions than by the Earth's rotation. While the Coriolis effect theoretically affects large-scale phenomena, it is typically overshadowed by factors like pre-existing water motion. Personal experiments, such as filling and emptying sinks, can reveal varying swirl directions based on these disturbances. Videos from channels like Veritasium and Smarter Every Day explore this topic further. Ultimately, the initial state of the water is the primary determinant of its swirling direction.
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I have a trivial question. What causes the direction in which the water in the spout turns? They say it's according to the Earth's hemisphere, but I don't really believe it and I'm looking for other reasons. Finally, even this reason would have to have some explanation.
 
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So, there is a theoretical effect due to the rotation of the earth. However, usually that is swamped by other disturbances like the initial state. So if there is only the slightest rotation already in the water before you start draining that will easily decide the rotational direction. Veritasium and Smarter Every Day did a video on this:

 
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Did you fill and empty the sinks in your house to see which way they swirl? What did you learn?
 
That I blocked the drain with a match.
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
This has been discussed many times on PF, and will likely come up again, so the video might come handy. Previous threads: https://www.physicsforums.com/threads/is-a-treadmill-incline-just-a-marketing-gimmick.937725/ https://www.physicsforums.com/threads/work-done-running-on-an-inclined-treadmill.927825/ https://www.physicsforums.com/threads/how-do-we-calculate-the-energy-we-used-to-do-something.1052162/
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