Motion Propagated Through Fluids on Superphysics

Proposition 41, Theorem 32

Mon, 01 Jan 0001 00:00:00 +0000

PROPOSITION 41. THEOREM 32

A pressure is not propagated through a fluid in rectilinear directions unless where the particles of the fluid lie in a right line.

Assume that the particles a, b, c, d, e lie in a right line.

Proposition 43, Theorem 34

Mon, 01 Jan 0001 00:00:00 +0000

Every tremulous body in an elastic medium propagates the motion of the pulses on every side right forward.

But in a non-elastic medium excites a circular motion.

Case. 1

The parts of the tremulous body, alternately going and returning, do in going urge and drive before them those parts of the medium that lie nearest, and by that impulse compress and condense them.

Proposition 44, Theorem 35

Mon, 01 Jan 0001 00:00:00 +0000

Assume that:

water ascends and descends alternately in the erected legs KL, MN, of a pipe.
a pendulum has a length between the point of suspension and the centre of oscillation equal to half the length of the water in the canal

The water will ascend and descend in the same times in which the pendulum oscillates.

Proposition 51, Theorem 39

Mon, 01 Jan 0001 00:00:00 +0000

Find the velocity of waves.

A pendulum’s length, between the point of suspension and the centre of oscillation, is equal to the width of the waves.

At the time that the pendulum will perform one oscillation, the waves will advance forward nearly a space equal to their width.

Proposition 51, Theorem 39

Mon, 01 Jan 0001 00:00:00 +0000

If pulses are propagated through a fluid, the several particles of the fluid, going and returning with the shortest reciprocal motion, are always accelerated or retarded according to the law of the oscillating pendulum.

Proposition 48, Theorem 38

Mon, 01 Jan 0001 00:00:00 +0000

The velocities of pulses propagated in an elastic fluid are in a ratiο compounded of the subduplicate ratio of the elastic force directly, and the subduplicate ratio of the density inversely;

Proposition 49 Theorem 11

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The density and elastic force of a medium being given, to find the velocity of the pulses.

Suppose the medium to be pressed by an incumbent weight after the manner of our air; and let A be the height of a homogeneous medium, whose weight is equal to the incumbent weight, and whose density is the same with the density of the compressed medium in which the pulses are propagated. Suppose a pendulum to be constructed whose length between the point of suspension and the centre of oscillation is A: and in the time in which that pendulum will perform one entire oscillation composed of its going and returning, the pulse will be propagated right onwards through a space equal to the circumference of a circle described with the radius A.

Proposition 50 Theorem 12

Mon, 01 Jan 0001 00:00:00 +0000

Find the distances of the pulses.

Let the number of the vibrations of the body, by whose tremor the pulses are produced, be found to any given time. By that number divide the space which a pulse can go over in the same time, and the part found will be the breadth of one pulse. Q.E.I.