Someone showering after exercise aboard a rotating space station spinning to simulate 1 gravity. How might Coriolis affect jets of water falling within a cubicle of 2 metres in height?

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    Welcome to Worldbuilding! Please have a look at the tour! In regards to your question: This depends heavily on the radius of the space station because the radius dictates the speed of rotation, which is dictating the force of the coriolis-effect. – DarthDonut Oct 15 at 14:50
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    I see, thanks, would you mind telling me how I can calculate that? If say the station were like a Kalpana but with a radius of 500m? And thanks for the welcome! – Chairman Yang Oct 15 at 14:54
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    Here's a site that does the calculation for you. artificial-gravity.com/sw/SpinCalc – Binary Worrier Oct 15 at 15:28
  • Thanks @BinaryWorrier! – Chairman Yang Oct 15 at 16:50
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    @Barmar youtube.com/watch?v=mXaad0rsV38 for a demonstration of it (with baby pools, not bathtubs). – Paŭlo Ebermann Oct 15 at 20:41
up vote 56 down vote accepted

As the water "falls" from shower head height towards the drain at the floor, it would be moving at a fixed velocity and be rotating slower than it should at the increased radius of the bottom of the shower, so it would tend to lag the rotation and bend backwards to the direction of spin.

The relative strength of this effect would be dependant on the overall habitat diameter. Larger habitats spin slower to simulate 1g, making the velocity gradient over a normal shower height smaller.

Paint circle of velocity

For example a 500 meter radius station (with 1g at 500 meters) with shower bottom at 500 meters and top at 498 meters, would have tangential velocity of 70.02 and 69.74 m/s at the bottom and top respectively. So the water leaving the shower would move anti spinward at ~0.28 meters/second. Given that the water would only take ~0.6 seconds to fall 2 meters it would move ~0.17 meters sideways. This distance could be noticable, but angling the showerhead or other simple design solutions could completely overcome the issue.

[Math done via SpinCalc, provided by Binary Worrier's comment]
Set radius at 500m and 1g, set radius to 498m and use the same angular velocity from the previous calculation.

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    Wow thanks for the diagram and explanation @Josh King, that's super useful – Chairman Yang Oct 15 at 16:51
  • Radius & Diameter both 500 m. in answer. Also, tangential velocity for 498 meters is not correct. Cleanup on aisle 3. – Gary Walker Oct 15 at 16:54
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    @GaryWalker, thanks for the corrections, fixed the diameter vs radius. The tangential for 498m radius is based on angular velocity from a 500 m radius and 1g so it is less than 1g at 498m giving the tangential velocity cited. – Josh King Oct 15 at 16:59
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    that 0.6 seconds suggests the water starts at rest, whereas it is likely to be moving at some speed... especially if you are worried about the Coriolis force causing dirty feet. based on water from my showerhead rising a metre, I'd say the time to fall would be around 0.35 seconds, so only 10 cm deflection at the foot. – JCRM Oct 16 at 15:12
  • I'd upvote this, but you've already gotten 46 votes since yesterday - and have certainly hit the daily rep-cap. Will UV tomorow if I remember :) – X-27 Oct 16 at 17:15

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