Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/134

§ 88 § 88. Fluid Pressure on a Body in Motion. — The pressure system about a body in motion in a fluid may be regarded as composed of two distinct component systems, i.e., the accelerative system, being that developed the instant a force is applied to a body at rest, which is essentially identical with the field of velocity potential, and the steady motion system, in which we have seen the fluid experiences a tension everywhere proportional to the energy density (compare "Dynamical Equations," § 59). The first of these is in evidence at the instant when the velocity is nil, as when a motion is started from rest or at the instant it is brought to rest; the second system belongs to the steady state when the disturbance is not subject to acceleration. For intermediate states when motion and acceleration are both present the two pressure systems are found compounded. A good illustration is to be found in the case of a body vibrating in a fluid under the influence of a spring, such as a vibrating rod. At the moment such a body is at the end of its motion, when the accelerative force is greatest, the pressure system is that due to the field of velocity potential; when it is in mid-stroke, that is when its velocity is greatest, the pressure system is that of steady state and follows the law already given.

The accelerative pressure system may (as has been already stated) be provided for, so far as the effect on the motion of the body is concerned, by the supposition of an appropriate addition to the mass, and the extent of this addition has already been given in certain typical symmetrical cases on the basis of the energy of the disturbance. When the impulse, as in the case of an oblique plane, is not in the direction of motion, it is not possible to account for the whole effect on the added mass basis, and in fact it is difficult to obtain a clear conception of the physical aspect of the problem in such unsymmetrical cases, and in general the solution is wanting. It would appear in the case of a plane possessing in itself no mass, that the motion on the application of a normal impulse borders on the indeterminate, for a tangential component, however small, would result in an