Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/154

§ 104 (2) That the discontinuous system may in a viscous fluid be regarded as arising by evolution from a motion initially obeying the mathematical equations.

(3) That in fluids possessing different values of kinematic viscosity the time taken for the evolution of the discontinuous system is greater when the kinematic viscosity is less, and vice versa.

(4) That the ultimate development of the discontinuous system of flow is more complete the less the value of the kinematic viscosity, and vice versa.

Taking the propositions in order:—

(1) Forces due to viscosity are proportional to velocity: when velocity is nil, such forces have no magnitude, consequently the initial direction of flow is unaffected by viscosity.

(2) In a viscous fluid it is established that the layer adjacent to the surface of a solid is adhesive, i.e., moves as part of the solid—that is to say, the viscous connection between fluid and solid is the same as that between two layers of fluid. Consequently when the flow has been established, there will be a layer of fluid next the solid more or less inert, which will only in a small degree partake of the motion of the dynamic system. Now the surface of the body possesses regions of greater and regions of less pressure, and this inert layer will be steadily pushed along the surface from the regions of greater pressure to those of less. Therefore, taking the typical case of a normal plane, the surface current of fluid so formed will be available to “inflate” the surfaces of hydrodynamic flow in the region of the edges, almost as if the edges of the plane were emitting fluid by volatilisation.

This inflation of the surfaces of flow in regions of least pressure can be conceived to continue until the combined inflated region becomes one whole, the “dead water,” occupying the space in the rear of the plane. Similarly for other forms of body.

(3) The less the viscosity the thinner the inert layer, and,