Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/29

Rh under pressure is, according to the kinetic theory, an example of the actual communication of momentum, and its pressure and the mean velocity can be correlated on the Newtonian principle; but once lose sight of the transference of matter (molecular motion), and we can only assert that the gas is exerting and transmitting force.

As a whole, the fluid, in the previous section, does not gain or lose momentum any more than does a cast-iron pillar supporting a load. The stress is transmitted in part by viscosity and in part dynamically; the part that is transmitted dynamically is transmitted by an actual transference of momentum from certain parts of the fluid to certain other parts; but this we cannot follow without equating the motions of the fluid throughout the whole of the enclosed space. The manner in which a portion of the stress is transmitted by viscosity may be compared, if we adopt a view put forward by Poisson and Maxwell, to its transference by a solid continually giving way in shear; or, on the other hand, if the fluid is gaseous, we may, on the kinetic theory, regard the viscous resistance as of purely dynamic origin, but belonging to a system quite apart from that of the aerodynamic disturbance.

§ 8. When the Newtonian Method is Applicable.—In the case of the Newtonian medium the quantity of matter dealt with, and momentum imparted per unit time, are defined quantities; but in the real fluid it has been shown that the motion produced is a circulation of the fluid not accompanied by any total change of momentum, and although parts of the fluid receive momentum in the direction of the applied force, other parts receive momentum in the opposite direction. In spite of this difficulty, there are certain cases in which the principle of the continuous communication of momentum can he, applied. A most striking example is to be found in the theory of marine propulsion founded by Rankine and Froude.

According to this theory the propeller (whether screw, paddle,