(04-23-2014, 06:44 PM)Strichev Wrote: That sounds interesting. Post the calculations for me (an uneducated individual in mathematics). I'm curious about the complexity of such matters. And whether I would understand them. Pancakes.
Cope that.
So, lets assume Coriolis acceleration (basically, we'll work with acceleration as a unit for Force to mass). That's given by 2(wXv) (X is the mathematical operator of cross), now, lets take the best case w and v are directly perpendicular to one anther, to get the best out of the cross operator, which means we are basically at one of the poles (doesn't matter which). So, our nice Coriolis acceleration would be 2(w*v) with the force's direction into the center of the sink's hole.
Now, lets find it. Our water particles are moving in a speed of about 10 CM/sec, which is 0.1 [Meter/Second]. Now, our w which is the rotational speed of the Earth is easy to calculate as 2pi/24 [1/hours] but we want to work in meters/second so lets transform it into seconds [2pi/(24*60*60)] (24 hours, 60 minutes in each hour, 60 seconds in each minute) that's 7.27*(10^-5).
So our Coriolis acceleration is ~1.5*(10^-5) [Meter/sec^2]
Now, lets check the gravity, and assume that whoever installed the sink hole didn't put directly horizontal to the earth. Lets check how accurate he must be, shall we?
Lets call our deviation degree a, and check how big is the acceleration that counters the Coriolis force.
so, for gravity we'll get g*sin(a), since it's likely a really small degree, we can safely assume sin a ~ a (in Radians, of course).
Lets assume g = 10 [Meter/sec^2] (it's slightly lower than that, but this is close enough as we are talking about size ratios here).
We get that our dear plumber that installed the sink must put the sink hole horizontally to the Earth in a deviation degree lower than 1.5*10^-6 radians.
Most likely that without using a microscope with some water to measure their deviation from being horizontal while installing the sink hole, and then letting a machine to do it (since even the tiniest shaking of the muscles, which occurs normally all the time) would create a bigger deviation.
Uhm...
I may be mistaken, but what you did was kind of calculated what kind of slant a surface must have to correspond to the coriolis force experienced by something going at a certain speed that you chose at random, at the rotational poles of the earth.
What you kind of didnt explain is why that would impact whether the coriolis force would be strong enough to make the water cycle in a certain direction while leaving the sink or not. Maybe I just didnt understand why, but I think that this angle actually doesnt matter, except maybe in some very special conditions, like the sink being totally flat and and the hole being at exactly the edge of the sink.
Without doing any calculations myself or thinking about it for too long, I'd say the thing that is most important thing for what direction the water cycles is:
1. If the water was already cycling before the plug was pulled. In a perfectly symterical round cylinder, if the water was already rotating faster than 1 revolution per day, the coriolis force will most likely not change the direction it was rotating in.
2. The shape of the sink. For example, if the sink has a relief/shape of a vortex or a spiral, it will probably affect the direction the water cycles more than anything else. Other shapes will also affect it, in less obvious ways.
But if the sink is a symetrical cylinder with a flat bottom, and the water isnt rotating at all relative to the earth surface before the plug gets pulled, I dont see how the angle of the cylinder would have an effect on which way the water should rotate, or how it should counter-act the coriolis force, from your explanation. when the water starts moving towards the hole in the sink, the coriolis force will deviate it slightly in one direction (either the left or the right of the motion, depending on which hemisphere you're on), which creates a slight clockwise or counterclockwise rotation while the water is exiting the sink. A slanted bottom of the sink would only affect the motion of the water and act against the coriolis force at a small region of the sink, while the coriolis force acts in all regions where the water is moving, so it seems that the solution cant really be that simple.
Not saying that you must be wrong, but as is your explanation doesnt really explain why your calculations are a proof.
Usually, in physics or engineering, we look at one particle, and from that we realize how a body of liquid or gas behaves, so, with your will lets go for that.
We assume that the sink hole is normal - a flat cylinder that has a simple symmetric (about so) curve all around it.
So, we look at a water particle that cycles the sink. It will, of course, have a sort of spiral course (not a perfect spire, which is what I will disproof shortly).
In my calculations I calculated the Coriolis force that would affect this particle in one of the Earth's poles, because in them Coriolis force would be the strongest (due to the cross operator, as if we look at the size of the force it would be 2*|w|*|v|*sin(alpha) with alpha being the degree between the two vectors, however in the poles, alpha would be pi/2 which yields us maximum Coriolis force. Gravity, due to its nature of always being in the direction of directly inside the sphere, is irrelevant of location.
So, lets look at our water particle, it has Coriolis force that is always in the direction of INSIDE the sink (aiming to its middle), however gravity, isn't just so.
If the sink hole is displaced from being directly horizontal to the Earth, in a system that is placed on the sink (e1,e2,e3, with e3 being the normal outside of the sink), it will also have a fraction of force that isn't just in e3, but also affecting e1,e2 plane.
That's the force I've calculated, and with which disproved that water in either side of the Earth cycle in one way or anther, it's completely unrelated to that, it's related to the shape of the sink. Thus, in your home you can have two sinks, one with water cycling cloakwise and one with water cycling counter-clockwise.