Bernoulli effect for spinning disks

[cyber one]

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"?

 

[rogerpendleto]

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.

 

[astrokreng]

I can provide some insights into the Bernoulli effect and its application to spinning disks. The Bernoulli effect is a well-known principle in fluid dynamics that describes the relationship between the velocity of a fluid and its pressure. In the case of a spinning disk, the air around the disk experiences a change in velocity due to the rotation of the disk, which results in a change in pressure.

In the case of a stationary disk, the air pressure on the platter is equal to atmospheric pressure. However, when the disk starts spinning at high speeds, the air near the surface of the disk experiences a decrease in pressure due to the increased velocity. This phenomenon is known as the Bernoulli effect.

In the example given, a spinning disk at 10,000 RPM would experience a significant decrease in pressure compared to a stationary disk. However, it is important to note that the pressure reduction is not solely due to the Bernoulli effect. The Ekman flow, which is the outward spiraling flow of air around the disk, also plays a role in reducing the pressure.

To estimate the percentage of atmospheric pressure that a spinning disk at 10,000 RPM would experience, we would need to consider various factors such as the size and shape of the disk, the density of the air, and the speed of rotation. Without this information, it is difficult to provide an accurate estimate. However, it is safe to assume that the pressure reduction would be significant and could potentially reach values close to 50% of atmospheric pressure.

In conclusion, the Bernoulli effect and Ekman flow both contribute to reducing the pressure experienced by a spinning disk. The exact percentage of atmospheric pressure that a spinning disk would experience would depend on various factors and would require further analysis and experimentation to determine accurately.