1.2 Viscosity

At the root is the governing laws. These are the equations of conservation; conservation of mass and momentum, at the present stage. Friction is an important element of fluid flow. In the absence of friction, a flat plate, dragged tangentially across the surface of a tank of water, would slide freely and induce no movement in the water. But, in the presence of friction, motion is communicated to the water adjacent to the plate and thence a circulation is established in the tank.

Friction internal to a fluid flow is characterized by viscosity. The viscosity coefficient, , is an empirical property of the fluid. For instance, a liquid is more viscous than a gas. As temperature increases, liquids flow more easily (think of tar, for example) so viscosity decreases with temperature. Gases have the opposite property, that viscosity increases with temperature. That behavior is less intuitive. It originates in the increased molecular agitation as temperature increases. Clearly, must be measured as a function of the fluid and of the temperature. In gases, the coefficient increases approximately as the square root of temperature; in liquids, it falls as the exponential of one over temperature [exp( E/ kT)]. Detailed formulas need not be discussed here. Values of for many fluids are available in computational fluid dynamics (CFD) codes and in handbooks. The magnitude of the viscosity is essential to determining flow regimes. Table 1.1 contains a few representative values at...