This may be several atmospheres at this point.
In fact v^2/r gives you the pressure gain. At M0.5 the pressure gain
will be of the order of 0.25 atmosphere. Very, very roughly Mach number
squared. The speed of sound is SQRT(E/P) where p is density and E is
elasticity. OK there are a few things like adiabatic compression and
the like but that is the order of magnitude.
You can't just 'pump out the air' and expect some sort of even result.
With ia circular can pressure is even (and in fact not too great - M0.5
is less than cabin pressure at 10,000m). Anyway what I did was to use
the thought experiment to illustrate a stable configuration. In fact if
you have the right configuration, involving blades the airflow will
naturally assume that configuration.
Tornados are the ones that do exist for a considerable time. Many
thousands of others start to form and collapse and never become a
tornado. Observant people can sometimes see these.
Indeed this is true. However the situation we have in one in which
energy is being continually supplied. The energy supplied will create
an energy momentum balance.
What one really needs to do is to run a test with fluid codes. We need
a large volume to get an accurate energy/momentum balance. Most fluid
simulations do not achieve a balance. This is perhaps a pity as a
number of air crashes have in fact resulted from persistent vortices
generated by large aircraft on take off.
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