applied to the plane C D per unit area to overcome the resistance of the fluid, we have—
F = µVl, 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,
![](http://upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Aerial_Flight_-_Volume_1_-_Aerodynamics_-_Fig_26.png/400px-Aerial_Flight_-_Volume_1_-_Aerodynamics_-_Fig_26.png)
Fig. 26.
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,
47