# How much acceleration does it take for water to flow downhill?

Assume a hab in outer space with 1 atmosphere pressure and 23ºC (comfortable room temperature),

To simulate gravity, the hab is spun. Acceleration is $\omega^2r$ where $\omega$ is angular velocity in radians/time and r is radius of hab.

Obviously the lower the "gravity", the smaller the hab can be. High rpm's make people sick and less gravity reduces the need for high rpm's. Also the structure doesn't need to be as strong.

I am wondering at what point gravity overcomes surface tension and water flows downhill. Thus the astronauts could enjoy showers, flush toilets, and their sinuses could drain.

• They probably want their toilettes to be designed to work in microgravity anyway, just in case the rpm thingy somehow fails. But in principle it is an interesting question. – LocalFluff Sep 10 '15 at 21:18
• It's not going to be a simple fixed value; the size of a water droplet and the hydrophilia of the surface it's on control whether it flows or not. Some old SF (possibly The Moon Is A Harsh Mistress?) described someone in 1/6g having to basically scrape water off themselves by hand; I don't know how closely the author worked the problem, but it seems plausible. – Russell Borogove Sep 10 '15 at 22:19
• As a thought experiment, a whole lake would tend to level itself in even minute gravity, while on Earth water drops do a perfectly fine job of sticking to glass windows in stubborn defiance of gravity. So the question would really have to be formulated in terms of how large a droplet (or body!) of water could form on a vertical glass surface (or some other criterion for "flowing downhill") – Blake Walsh Sep 10 '15 at 23:56
• – Russell Borogove Sep 11 '15 at 0:58
• To summarize @Blake, the answer could be anywhere to an infinitesimal positive quantity or less (negative). I don't understand this question; it seems more like "how much gravity to make things kinda-sorta normal" versus "how much acceleration does it take for water to flow downhill" (to which the answer is any). – Nick T Sep 11 '15 at 1:49

Roman aqueduct engineers used a typical gradient of 1:4800, which is about 20cm per km. The equivalent acceleration is about $2 mm/s^2$. So not very much is required to keep the water flowing.