Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/67

Rh applied to the plane C D per unit area to overcome the resistance of the fluid, we have—

F = µ$V⁄l$, where µ is a quantity termed the coefficient of viscosity.

This equation is merely the algebraic expression of the law previously stated, for where V and l are unity we have F = µ.

It will be seen that between the planes A B and C D there will exist a velocity gradient. A series of particles situated at points on a straight line a, a, a, a, at one instant of time, will be situated at points b, b, b, b, on another straight line at another instant,



the figure thus giving a pictorial idea of the motion in a viscous fluid.

§ 33. Viscosity in relation to Shear.—In the foregoing illustration, which is in substance as given by Maxwell, the nature of viscous strain as a shear is sufficiently obvious. There are cases, however, in which viscosity plays a part in which the conditions are not so straightforward. The modern definition of shearing stress is stress that tends to alter the form of a body without tending to alter its volume, and any strain that involves the geometrical form or proportions of a body requires shearing stress for its production. All stresses and strains can be resolved into shear and dilatation (plus or minus); and such stresses as linear tension or compression of a solid involve stress in shear.

We thus see that changes in the shape of a body of a fluid,