In the case of the field proper to a force of stated direction applied to a given body in a quiescent fluid, it follows from considerations belonging to hydrodynamic theory that the form of the field is unique, that is to say, its geometry is absolutely defined by the conditions.
In the case of a fluid in an arbitrary state of disturbance, the field of force will not generally be of the same form as for the quiescent state. Where there is pre-existing motion in the fluid we may speak of the field as a distorted field.
The form of the field in the case of a fluid initially at rest for such forms as a sphere, an ellipsoid, or a circular or elliptical cylinder, is perfectly well known (§ 79), and in an infinite expanse of fluid extends indefinitely in every direction. If, however, the region is bounded as in the case of the atmosphere, limited by a rigid boundary constituted by the surface of the earth, the field will be modified as represented diagrammatically in Fig. 63, in which the continuous lines are the lines of force, and the dotted lines, normal to the former, are lines or surfaces of equal pressure.[1]
It is a necessary consequence of the definition of lines of force that all lines in the immediate vicinity of a stationary boundary surface must be parallel to it, and therefore that surfaces of equal pressure, if they meet the ground, must do so normally, as indicated in Fig. 63. This figure will consequently represent diagrammatically the spreading out of the pressure area and its ultimate distribution as a region of increased pressure on the surface of the earth.
§ 114. Flight with an Evanescent Load.—We will now suppose that the aerofoil that gives rise to the field of force is in flight, that is to say, it possesses a horizontal velocity. Now we know at present very little of the nature of the disturbance created. We cannot even assert that the form of the resulting flow is
- ↑ Compare § 60. Lines of equal pressure only for initial motion otherwise correspond to const. of mathematical theory.
150
