Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/26

§ 5 The nature of this difficulty is clearly demonstrated by the following proposition:— When a body, propelled through an incompressible fluid, contained within a fixed, enclosure, experiences resistance to its motion, the force exerted by the body on the fluid does not impart momentum to the fluid, but is transmitted instantly to the confines of the fluid however remote, and is wholly borne by its boundary surfaces.

Let us suppose (Fig. 1) a body which we will take to be a normal plane C, acted upon by a force F in an enclosure A,



filled with fluid B. The enclosure may be supposed as large as we please, or, in the limit, infinite in its dimensions.

Then the condition that the enclosure is fixed denotes that the force F applied to the plane is applied from the walls of the enclosure; for, if we suppose it applied from without we can resolve the force into a force acting between the plane and the enclosure F F1, and a force of equal magnitude acting from without on the enclosure FII, and since the enclosure is fixed the latter can have no effect.

Now since the fluid is incompressible its density is constant and uniform, therefore the mass centre of the contents cannot move relatively to the enclosure; and the enclosure itself is fixed, consequently the fluid in sum does not receive momentum.