Nutritional value of apricots
Coriolis rotation can conceivably play a role on scales as small as a crapper. It is a commonly held myth that the every-day rotation of a bathtub or toilet vortex is due to whether one is in the northern or southern hemisphere. An article in Nature, by Ascher Shapiro, describes an experiment in which all other forces to the system are removed by filling a 6 ft. tank with water and allowing it to settle for 24 hrs (to remove any internal velocity), in a room where the temperature has stabilized (temperature differences in the room can introduce forces inside the fluid). The drain plug is then very slowly removed, and tiny pieces of floating wood are used to observe rotation. During the first 12 to 15 minutes, no rotation is observed. Then, a vortex appears and consistently begins to rotate in a counter-clockwise direction (the experiment was performed in the Northern hemisphere, in Boston, MA). This is repeated and the results averaged to make sure the effect is real. The Coriolis effect does indeed play a role in vortex rotation for draining liquids that have come to rest for a long time.
In reality, this experiment shows that the Coriolis effect is a few orders of magnitude smaller than various random influences on drain direction, such as the geometry of the container and the direction in which water was initially added to it. In the above experiment, if the water settles for 2 hrs or less (instead of 24), then the vortex can be seen to rotate in either direction. Most toilets flush in only one direction, because the toilet water flows into the bowl at an angle. If water shot into the basin from the opposite direction, the water would spin in the opposite direction.
The idea that toilets and bathtubs drain differently in the Northern and Southern Hemispheres has been popularized by several television programs, including The Simpsons "Bart vs. Australia, and the The X-Files episode "Die Hand Die Verletz.
Several science broadcasts and publications, including at least one college-level physics textbook, have also stated this. Some sources that incorrectly attribute draining direction to the Coriolis force also get the direction wrong, claiming that water would turn clockwise into drains in the Northern Hemisphere.
The Rossby number can also tell us about the bathtub. If the length scale of the tub is about L = 1 m, and the water moves towards the drain at about U = 60 cm/s, then the Rossby number is about 6 000. Thus, the bathtub is, in terms of scales, much like a game of catch, and rotation is unlikely to be important.
In purely non-vector terms: at a given rate of rotation of the observer, the magnitude of the Coriolis acceleration of the object is proportional to the velocity of the object and also to the sine of the angle between the direction of movement of the object and the axis of rotation.
The vector formula for the magnitude and direction of the Coriolis acceleration is:
[omitted in the interest of brevity] lol
where v is the velocity of the particle in the rotating system, and is the angular velocity which has magnitude equal to the rotation rate and is directed along the axis of rotation of the rotating reference frame, and the symbol represents the cross product operator.
The equation may be multiplied by the mass of the relevant object to produce the Coriolis force:
.
Fictitous Force would be a derivation.
The Coriolis effect is the behavior added by the Coriolis acceleration. The formula implies that the Coriolis acceleration is perpendicular both to the direction of the velocity of the moving mass and to the frame's rotation axis. So in particular:
if the velocity is parallel to the rotation axis, the Coriolis acceleration is zero.
if the velocity is straight inward to the axis, the acceleration is in the direction of local rotation.
if the velocity is straight outward from the axis, the acceleration is against the direction of local rotation.
if the velocity is in the direction of local rotation, the acceleration is outward from the axis.
if the velocity is against the direction of local rotation, the acceleration is inward to the axis.
The vector cross product can be evaluated as the determinant of a matrix
Shitter water has the potential to flow either clock-wise OR counter-clock-wise, regardless of latitudinal or longitudinal influences.
How's that for off-topic, Alan? :thumbleft:
"Wade" wrote: