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Full text of "Scientific Papers - Vi"

1914]                                               FLUID MOTIONS                                             249
In conclusion, I must touch briefly upon a part of the subject where theory is still at fault, and I will limit myself to the simplest case of alló the uniform shearing motion of a viscous fluid between two parallel walls, one of which is at rest, while the other moves tangentially with uniform velocity. It is easy to prove that a uniform shearing motion of the fluid satisfies the dynamical equations, but the question remains: Is this motion stable ? Does a small departure from the simple motion tend of itself to die out ? In the case where the viscosity is relatively great, observation suggests an affirmative answer; and 0. Reynolds, whose illness and comparatively early death were so great a loss to science, was able to deduce the same conclusion from theory. Reynolds' method has been improved, more especially by Professor Orr of Dublin. The simple motion is thoroughly stable if the viscosity exceed a certain specified value relative to the velocity of the moving plane. and the distance between the planes; while if the viscosity is less than this, it is possible to propose a kind of departure from the original motion which will increase for a time. It is on this side of the question that there is a deficiency. When the viscosity is very small, observation appears to show that the simple motion is unstable, and we ought to be able to derive this result from theory. But even if we omit viscosity altogether, it does not appear possible to prove instability a priori, at least so long as we regard the walls as mathematically plane. We must confess that at the present we are unable to give a satisfactory account of skin-friction, in order to overcome which millions of horse-power are expended in our ships. Even in the older subjects there are plenty of problems left!ethod would be an accurate one. for the comparison of viscosities. The change in the ratio of head to suction, is rather slow, and the measurement is usually somewhat prejudiced by unsteadiness in the. suction manometer. Possibly better results would be obtained in more elaborate observations by several persons, the head and suction being.recorded separately and referred to a time scale so as to facilitate interpolation. But as they stand the results suffice for my purpose, showing, directly and conclusively the influence of viscosity as compensating a, change'.in otKe velocity. , .ies are small in comparison with that of sound.