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The terms involving square roots can be expressed as elliptic integrals (13) of the first ( F ) and second ( E ) kind. Thus In any system where solids are to fall through or are to be lifted by %uids a knowledge of the slip velocity of the solids is of great importance. At present there is a definite lack of experimental data in the literature for fluid-solid systems. The present work ( 2 ) in the intermediate or transition region between where the Stokes and Newton laws apply has been carried out to develop an accurate equation for slip velocity calculations for both spherical and nonspherical particles. THEORYThe slip velocity of a single body falling in a fluid is defined as the constant equilibrium velocity attained by the body when the resistance offered by the viscous medium increases to the point where it is equal to the sravitational acceleration force. If the fluid is also stationary and infinite, the slip velocity equals the terminal velocity.It has been demonstrated experimentally (4) that the resistance cp of a particle in motion involves four quantities: the surface area of the particle A,, its terminal veloc-H. Donald Allendorf is with Aerochem Research Laboratories, Inc., Princeton, New Jersey. Page 1070A.1.Ch.E.475 jb./c,u. ft.), surface to 0.31 Ib./cu. ft.) were ity ut, and the viscosity pf and density ,of of the medium through which the particle is flowing. The relationship involved may be expressed by the following equation:It should be noted that the area used here is the actual surface area of the particle rather than the area of the particle projected on a plane perpendicular to the direction of flow as used by several previous investigators. The actual area was chosen as it is much more readily detgmined experimentally.

The usefulness of the theorem of corresponding states has been extended to include polar substances. The parachor is used as a fourth parameter to characterize molecular size-shape; the acentric factor, used as the third parameter, is a measure of molecular size-shape, polarity, quantum influence, and hydrogen bonding. These two parameters were combined empirically in a polynomial expansion to separate molecular size-shape effects from the association effects. The effectiveness of this separation was demonstrated by using this four-parameter theorem to generalize the Frost-Kalkwarf vapor pressure equation. Vapor pressures may be predicted from a knowledge of only the critical temperature, critical pressure, acentric factor, and parachor. An average deviation of 4.92% was obtained for 5952 vapor pressure data points representing 242 substances.CHEMICAL ENGINEERS must deal with many types of fluids in the development, design, and operation of chemical plants. I t is essential to know the physical and thermodynamic properties of these fluids as accurately as possible in order to determine equipment sizes, energy requirements, equilibrium yields, and separation ratios. Furthermore, this information can be best utilized in the areas of optimization and process control if it is represented as an analytical function of a process variable. For these reasons accurate correlations of these properties are becoming increasingly important.Although many correlations are available, there is very little uniformity among them. Different correlating parameters are required depending on the property being correlated and, in some instances, the temperature or pressure range represented. Many of these correlations were developed specifically for one substance by empirically determining specific coefficients for a given substance. The generalized correlations which use the same characterizing parameters for all properties and conditions are based on the theorem of corresponding states. Corresponding State ExtensionsThe early work of van der Waals used the critical temperature and pressure to characterize a substance. According to the simple theorem of corresponding states, two substances a t equal reduced conditions should behave identically. This has been shown to be valid only for spherical, noninteracting (simple) substances; however, Riedel (1954), Pitzer et al. (1955), Su (1946), and Lydersen et al. (1955) added a third parameter to the theorem I Present address, Research and Development Department, Continental Oil Co., Ponca City, Okla. 74601to correct it for nonidealities due to molecular size-shape. The result was a considerable improvement in the theorem for nonpolar substances. The most popular third parameter was the Pitzer et al. acentric factor, W . The acentric factor is used to correct the value of a physical property for a simple fluid:where G is any correlatable property, G o is a simple fluid property, and G Basically, the acentric factor is a measure of vapor pressure deviations from the simple fluid, caused by size...