Bernoulli effect for spinning disks

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cyber one

Main Question or Discussion Point

For a stationary disk, the air pressure on the platter is atmospheric
pressure.

For a disk spinning at 10,000 RPM, say 140 miles per hour for a 5.25
inch disk, I assume the Bernoulli effect would reduce the pressure,
but because of the Ekman flow, the pressure would be more than the
pressure would be on a non-rotating disk in which the air was moving
over the disk surface linearly at 120 miles per hour.

The so-called no-slip property of gas-solid interfaces requires that
the gas in the immediate vicinity of a spinning disk move with the
disk. Unlike the solid comprising the disk, however, the gas spinning
with the disk cannot withstand the concomitant centrifugal force. The
resulting outward spiraling flow is called Ekman flow.

Can you give me an approximate estimate of the percentage of
atmospheric pressure a spinning disk platter at 10,000 RPM would
"experience"?
 

Answers and Replies

  • #2
The static pressure on a spinning disk is the same as the static pressure on a stationary disk. The Bernoulli Theorem is greatly missunderstood. In the classical classroom demonstration the difference in pressure across a restriction is caused by the increased pressure in front of the restriction not the reduced pressure due to increased velocity after the restriction. There is no reduction in static pressure due to air moving parallel to a surface. Try this experiment - Lay a piece of FLAT paper on a porous surface (Grill Pan) blow air over it with a powerful blower - IT WILL NOT LIFT as Bernoulli would have us believe. Similarly aircraft lift has nothing to do with Bernoulli but caused by the angular acceleration of the air (Coanda Effect) causing low pressure areas as the air which has finite mass tried to bend to follow the curvature of the wing.
 

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