In a Spirit of Harmony (was - Age of Universe...)

In article ,
(Bill Sheppard) wrote:

Painius wrote,

...i'm still having a problem with the same thing Odysseus
challenged... remember,.. when you read "disappear", don't assume that
Odysseus is talking about the roach-motel issue...

Near as i can read his point, he's talking about the flow "disappearing"
in cross section, "compressing" in other words. Take the airflow going
down a carburetor throat; it "disappears", "compresses" in cross section
while elongating, stretching axially. Or take a funnel; the flow going
down a funnel "disappears" in cross section, yet at every cross section,
the same number of "grains per second" are passing thru every cross
section.. while the flow elongates and accelerates axially.

Of course, but it does so *by a specific amount*, and I believe I've
demonstrated upthread that your scenario is inconsistent. In comparing
planets of various sizes and densities Painius is seeing a related
problem.

If you multiply the rate of flow at the mouth of a funnel, or a
constriction in a pipe, by its cross-section, and do the same at the
narrowest point, you should get an identical figure -- assuming the
volume flux is constant. Between the widest point and the neck, the
velocity of the fluid must increase to match the decrease in
cross-sectional area. In the case of a spherical field, the
inverse-square law follows from this geometrical principle.

If you didn't follow the previous calculation, let's look a 'unit' of
flowing space as it heads toward the isolated Earth from the altitude of
the Moon's orbit. The escape velocity at r = 3.84E8 m is

v_esc = sqrt(2GM/r)

= sqrt(2 * 6.67E-11 * 5.97E24 / 3.84E8) m/s

= 1440 m/s.

So our test subject starts out at 1.44 kilometres per second, but must
accelerate as it moves inward, as it's 'constricted' by the decreasing
cross-section. By the time it nears the surface the radius is down to
6.4E6 m / 3.84E8 m = 1/60 of the starting figure, reducing the area to
1/3600 of the initial sphe accordingly, we'd expect it to move 3600
times as fast as it was when we began following it. That would be nearly
5200 km/s -- but the escape velocity here is only 11.2 km/s, five
hundred times slower! Again, I believe this is what Painius was getting
at when he referred to "slamming on the brakes" -- at the very least
it's a case of "too light on the gas-pedal".

--
Odysseus