Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/73

Rh and we have the unexpected but experimentally established result that the resistance does not vary with the area, hut according to a fractional power of same.

If, as is customarily assumed, the resistance of a body is taken as proportional to the square of the velocity, then we shall have q = zero, and the pressure is independent of viscosity altogether; this result is due to Allen. Under these conditions the resistance is directly as the area, and conversely if viscosity have any influence on the resistance, then the resistance cannot vary directly as the area, hence the existence of viscosity may be regarded as giving a definite scale to the fluid.

§ 37. Turbulence.—The steady state of viscous motion depicted in Figs. 26 and 27, on which the laws of viscosity and skin-friction have been based, is found in practice to obtain over a moderate range of velocity only. When a certain critical velocity is exceeded the continuity becomes broken and the phenomenon of turbulence manifests itself. Under conditions involving pure viscosity (in contradistinction to the more complex phenomenon of skin-friction), this critical point has been investigated experimentally by Mr. Osborne Reynolds in the case of liquid flowing through a straight tube. It is found that up to a certain velocity the flow is everywhere parallel to the axis, but when this critical velocity is reached the parallel flow breaks up, and is replaced by an irregular turbulent motion. Up to the critical velocity the law deduced by Poisouille for viscous flow through a tube holds good; beyond this point the resistance rises more rapidly, and for high velocities approximates to F varies as V2, when the energy is mostly expended in generating the turbulent motion.

The method of investigation employed by Osborne Reynolds consisted of observing the behaviour of a coloured filament of liquid introduced in the centre of a tube containing liquid in motion; the result obtained is that steady motion ceases to exist