such as take place in the course of its passage through a "tube of flow" in the vicinity of a streamline body, are resisted by viscosity in proportion to the velocity with which the change of form takes place, and the work done on the fluid in this manner must be supplied by a propulsive force; that is to say, the body will be resisted in its motion through the fluid from the cause stated. We have here one of the causes of viscous resistance.
We cannot state that this form of resistance will increase directly as the velocity, that is, according to the viscous law, for we do not know that the form of the lines of flow is the same at different velocities. It would appear that this must be so for an inviscid fluid. It would also seem evident that the viscous resistance will modify the form of flow materially. It may therefore be deduced that the form of flow will be more modified for low than for high velocities, in which case the form of resistance we are now discussing will not vary exactly in the direct ratio of the velocity.
Bodies other than of streamline form will also be affected by this type of viscous resistance, when it will appear as an added resistance. The only exception is found in the case of a plane moving tangentially, the consideration of which introduces the important subject of skin-friction.
§ 33. Skin-friction.—It is well established that there is no slipping of a fluid past the surface of a solid, but that the film adjacent to the surface adheres to it, and the resistance experienced is of the nature of a viscous drag. This fact has already been assumed in the discussion of the law of viscosity, for otherwise there would be no necessity for the fluid to be set in motion by the plane C D at all. To a certain extent, therefore, the term "skin-friction" is misleading. It is, however, a term sanctioned by usage, and it is difficult to find a more suitable expression.
Let us suppose that a plane having no sensible thickness be put in motion tangentially through a fluid, and be maintained in motion until a steady state is reached. Then the advancing edge
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