The Circular Motion of Fluids on Superphysics

Proposition 51, Theorem 39

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HYPOTHESIS

The resistance from the lack of lubricity in a fluid is proportional to the speed of the separation of the fluid’s parts.

Proposition 52, Theorem 40

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Assume that:

a solid sphere in an uniform and infinite fluid revolves around an axis given in position with a uniform motion
the fluid is forced around by only this impulse of the sphere
every part of the fluid perseveres uniformly in its motion.

The periodic times of the parts of the fluid are as the squares of their distances from the sphere’s centre.

Corollaries

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COROLLARY 1

Hence:

the angular motions of the parts of the fluid around the axis of the globe are reciprocally as the squares of the distances from the globe’s centre.
the absolute velocities are reciprocally as the same squares applied to the distances from the axis.

COROLLARY 2

Assume that a globe revolves with a uniform motion around an axis in a similar and infinite quiescent fluid with a uniform motion.

Scholium

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I have supposed the fluid to consist of matter of uniform density and fluidity.

A globe placed anywhere in the fluid may propagate with the same motion of its own, at distances from itself continually equal, similar and equal motions in the fluid in the same interval of time.

Proposition 53, Theorem 41

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Bodies carried around in a vortex, and returning in the same orb, are of the same density with the vortex.

They are moved according to the same law with the parts of the vortex, as to velocity and direction of motion.