[Rhodes22-list] Fluid Dynamics

[Ronald Lipton]

Brad,

    It turns out that the original explanation is due to Einstein.
The story goes that he was asked by the wife of Erwin
Schrodinger (of wave equation and the cat that is both
dead and alive) why tea leaves congregate at the center
of the cup. She said she asked her husband and he couldn't
answer - "why don't you ask Einstein, he thinks he's so
smart" he might have said.

One would expect that the centrifugal force, induced by
stirring, would propel the leaves outward.  However
in the case of a teacup the rotation of the fluid near the bottom
is slowed by friction with the bottom surface of the cup (the
boundary layer).  The centrifugal force is proportional to the rotation
velocity squared, so water is pushed outward much more
at the top of the cup then the bottom.  This sets up a
circulation pattern where water flows outward near the top,
falls to the bottom near the rim, flows inward at the bottom,
and flows up at the center.  Thus tea leaves near the bottom are
carried along with the return flow and congregate at the
bottom.

Ron
On Jan 16, 2006, at 8:19 PM, brad haslett wrote:

> Ron,
>
> Would you educate us on  'the "tea leaf" problem'?  We
> just went through a major rewrite on the DC10 manual,
> an airplane that's been around for 25 years, with a
> whole new  formula to adjust V approach (Vapp)for
> gusty winds.  I went through a presentation with 11
> slides with other instructors today and the general
> response was "what the f**!" is that all about."  "You
> know, 1.3 times V stall (Vs), plus one knot for
> granny, two for Wilbur and Orville, one more for each
> child, etc., just don't run off the end of the runway
> with the extra speed."  The next time I have to
> present this program I'd love to respond, "you know,
> just like the 'tea leaf' problem."  No doubt there
> will be at least one Zoomie grad (Air Force Academy)in
> class with a degree in aerodynamics who will want to
> debate "tea leaves".
>
> Brad
>
> --- Ronald Lipton <rlipton at earthlink.net> wrote:
>
>> Bill,
>>
>>     In general there is a boundary layer between a
>> solid object and
>> fluid flowing around it.  Typically this is analyzed
>> to understand the
>> sources of drag on a hull, which are dependent on
>> the relative
>> velocities, the viscosity of the fluid, and whether
>> the flow is laminar
>> or turbulent.  The actual smoothness of the hull has
>> only a minor
>> effect.  The molecular layer adjacent to the hull is
>> considered as
>> moving at the hull velocity, there is then a
>> boundary layer where the
>> velocity of the the water increases to the velocity
>> of the stream.
>> For a hull moving through water at ~5 knots the
>> boundary layer is
>> a few millimeters.  It may be a bit larger in a
>> river, but if the bed
>> has
>> few large obstacles it is hard to see how there
>> would be a large
>> enough turbulent boundary layer the tumble an
>> anchor.  the problem
>> is different if there is a bend or obstruction in
>> the river with changes
>> the direction of flow.
>>
>> By the way one of the nice applications of the
>> boundary layer concept
>> is the "tea leaf" problem, which analyzes the reason
>> tea leaves
>> congregate
>> at the center of a teacup after stirring in terms of
>> boundary layer
>> effects.
>>
>>
>> Ron
>>
>>
>>
>> On Jan 16, 2006, at 7:06 PM, Bill Effros wrote:
>>
>>> Here's the fluid dynamics part.  As I understand
>> eddies, they occur
>>> because the water is not one solid mass flowing at
>> a constant speed.
>>> I think the water can move faster at the surface
>> than the bottom.  So
>>> if you drop an anchor it encounters turbulence
>> which may cause it to
>>> tumble or spin on the way to the bottom, but the
>> water may be
>>> traveling far more slowly at the bottom allowing
>> the anchor to set at
>>> a much slower speed than the boat is moving.
>>>
>>> I could be completely wrong about this.
>>
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