On the effect of the internal friction of fluids on the motion of pendulums / by G.G. Stokes.

  • Stokes, George Gabriel, 1819-1903.
Date:
1851
Catalogue details

Licence: Public Domain Mark

Credit: On the effect of the internal friction of fluids on the motion of pendulums / by G.G. Stokes. Source: Wellcome Collection.

Provider: This material has been provided by The Royal College of Surgeons of England. The original may be consulted at The Royal College of Surgeons of England.

    54/104 (page 50)
    Now the general character of the motion must be nearly the same whether the velocity of the cylinder be constant, or vary slowly with the time, so that it does not vary materially when the cylinder passes through a space equal to a small multiple of its radius. To return to the problem considered in Section III., it would seem that when the radius of the cylinder is very small, the motion which would be expressed by the formulae of that Section would be unstable. This might very well be the case with the fine wires used in supporting the spheres employed in pendulum experiments. If so, the quantity of fluid carried by the wire would be diminished, portions being continually left behind and forming eddies. The resistance to the wix’e would on the whole be increased, and would moreover approximate to a resfstance which would be a function of the velocity. Hence, so far as depends on the wire, the arc of oscillation would be more affected by the resistance of the air than would follow from the formulae of Section III. Whether the effect on the time of oscillation would be greater or less than that expressed by the formulae is difficult to say, because the increase of resistance would tend to increase the effect on the time of vibration, while on the other hand the approximation of the law of resistance to that of a function of the velocity would tend to diminish it. Section V. On the effect of internal friction in causing the motion of a fluid to subside. Applica- tion to the case of oscillatory waves. 49. We have already had instances of the effect of friction in causing a gradual subsi- dence in the motion of a solid oscillating in a fluid; but a result may easily be obtained from the equations of motion in their most general shape, which shews very clearly the effect of friction in continually consuming a portion of the work of the forces acting on the fluid. Let Pi, Pg, P3 be the three normal, and Pi, P3 the three tangential pressures in the direction of three rectangular planes parallel to the co-ordinate planes, and let D be the symbol of differentiation with respect to t when the particle and not the point of space remains the same. Then the general equations applicable to a heterogeneous fluid, (the equa- tions (10) of my former paper,) are \Dt dP^ dT^ dT^ _ dx ^ dy ^ dz ’ (132) with the two other equations which may be written down from symmetry. The pressures Pi, 8ec. are given by the equations P^ = p-2fx du dx /dv dw\ Pi — ~ M { -r~ + \dz dy} (133) and four other similar equations. In these equations du dv dw dx dy dz (134)