## VISCOSITY DEFINITION AND BASIC INFORMATION

The quantities such as pressure, temperature, and density discussed in the previous section are primary thermodynamic variables characteristic of any system. There are also certain secondary variables which characterize specific fluid-mechanical behavior.

The most important of these is viscosity, which relates the local stresses in a moving fluid to the strain rate of the fluid element.

When a fluid is sheared, it begins to move at a strain rate inversely proportional to a property called its coefficient of viscosity (u)  . Consider a fluid element sheared in one plane by a single shear stress , as in Fig. 1.4a.

The shear strain angle will continuously grow with time as long as the stress is maintained, the upper surface moving at speed (d u) larger than the lower. Such common fluids as water, oil, and air show a linear relation between applied shear and resulting strain rate

Equation (1.23) is dimensionally consistent; therefore has dimensions of stress-time: {FT/L2} or {M/(LT)}. The BG unit is slugs per foot-second, and the SI unit is kilograms per meter-second. The linear fluids which follow Eq. (1.23) are called newtonian fluids, after Sir Isaac Newton, who first postulated this resistance law in 1687.

The viscosity of newtonian fluids is a true thermodynamic property and varies with
temperature and pressure. At a given state (p, T) there is a vast range of values among the common fluids. Table 1.4 lists the viscosity of eight fluids at standard pressure and temperature.

There is a variation of six orders of magnitude from hydrogen up to glycerin. Thus there will be wide differences between fluids subjected to the same applied stresses.

Generally speaking, the viscosity of a fluid increases only weakly with pressure. For example, increasing p from 1 to 50 atm will increase of air only 10 percent. Temperature, however, has a strong effect, with increasing with T for gases and decreasing for liquids. Figure A.1 (in App. A) shows this temperature variation for various common fluids. It is customary in most engineering work to neglect the pressure variation.

The variation (p, T) for a typical fluid is nicely shown by Fig. 1.5, from Ref. 14, which normalizes the data with the critical-point state ( c, pc, Tc). This behavior, called the principle of corresponding states, is characteristic of all fluids, but the actual numerical values are uncertain to 20 percent for any given fluid.