Viscosities available in the literature for the gaseous and liquid states of eleven substances have been correlated with reduced density by the use of dimensional analysis and the Abas-rade expression for the residual viscosity to produce a single generalized relationship which is presented both graphically and analytically. The substances are argon, nitrogen, oxygen, carbon dioxide, sulfur dioxide, methane, ethane, propane, i-butane, n-butane, and n-pentane. The properties required for the calculation of viscosity with this relationship are the molecular weight, the critical constants, and the density of the substance a t the temperature and pressure considered.Separate relationships were developed for hydrogen, ammonia, and water which do not follow the consistent behavior of the other substances. Viscosity values for ethylene calculated with the generalized relationship compared favorably with the corresponding experimental values.In 1944 Uyehara and Watson developed a generalized correlation for the prediction of the viscosity of a pure substance at any temperature and pressure ( 7 9 ) . Although this correlation has proved to be of extreme utility for industrial calculations, current demands for highly accurate viscosity values in such areas as heat transfer and reactor design necessitate the development of a more exacting method for obtaining viscosities of both gases and liquids.Recent studies on the prediction of the transport properties of pure substances have been primarily concerned with the viscosity and thermal conductivity of gases at normal pressures (47, 74, 7 5 ) . Using a dimensional analysis approach and viscosity data reported in the literature for fifty-two nonpolar and fifty-three polar gases, Stiel and Thodos (74, 7 5 ) have developed relationships which can easily be applied for the prediction of the viscosity of any pure gas at moderate pressures (0.1 to 5 atm.). For nonpolar gases the following relationships resulted: (2), (3), and (4) for all the substances investigated were found to compare favorably with the corresponding experimental values. Therefore it would be desirable to utilize a similar approach to develop relationships for the prediction of the viscosity of pure substances at high pressures in both the gaseous and liquid states.In 1952 Abas-zade (1) proposed that the following relationship exists between the residual thermal conductivity of a liquid and its corresponding density:Thodos and co-workers (23, 33, 50, 66, 68) have studied the transport properties of several individual substances over a complete range of temperatures and pressures and have found that Equation (5) and a similar expression for the residual viscosity

Experimental measurements have been conducted to establish a correlation for the settling velocities of cylindrical particles whose length to diameter ratios varied from 10 to 1/10 and Reynolds numbers between 200 and 60,000. It was found that separate correlations exist for cylinders of L/D > 1.0 and for L/D < 1.0. These relationships are expressed analytically and were found to be independent of the Reynolds number. In addition, a qualitative description of the motion generated by the particle during settling has been discussed for cylinder of L/D less than, equal to, and greater than one.

In 1949 Gamson (13) produced a reduced state correlation from available thermal conductivity data in which the reduced thermal conductivity, k/kc, is plotted against reduced temperature and pressure. Experimental data, which were subsequently obtained, were found to deviate considerably from values resulting from Gamson's correlation ( 4 5 ) . Comings and Nathan (9) combined the Enskog relationships for viscosity and thermal conductivity to obtain an expression for the ratio, k/k", in terms of the viscosity ratio, p /~" , and the quantity, y. In the resulting relationship, the effects of the internal degrees of freedom of the molecules are neglected. Values of y were obtained from experimental P-V-T data as suggested by Enskog (lo), and experimental and calculated viscosities were used to develop a correlation between k/k* and reduced temperature and pressure. Lenoir and Comings (29) found that their experimental thermal conductivities for argon, nitrogen, methane, ethylene, and carbon dioxide were in good agreement with those resulting from the correlation of Comings and Nathan. Lenoir, Junk, and Comings (30) used their experimental values for nitrogen, methane, and argon, and the values obtained previously by Lenoir and Comings to develop a new correlation for k/k* which is very similar to that of Comings and Nathan, except that it predicts higher values for conditions in the vicinity of the critical point. Thermal-conductivity values determined by Lenoir, Junk, and Comings for ethane were found to be inconsistent with corresponding values resulting from their correlation, as were the subsequent values obtained by Leng and Comings (28) for propane and those of Kramer and Comings (27) for n-butane. Therefore, it would be desirable to develop an improved correlation for thermal conductivity which is also applicabIe to a wider range of substances.Jossi, Stiel, and Thodos (20) have obtained reliable expressions for the viscosity of pure substances in the dense gaseous and liquid phases by the use of a relationship between the residual viscosity, p -EL*, and density, along with a dimensional analysis approach. Thodos and coworkers (22, 38, 47, 48) have found that the residual thermal conductivity, k -k*, is a unique function of density for all the substances investigated. A theoretica1 basis for such a dependence has been provided by Predvoditelev (41). Therefore, in the present study an approach similar to that of Jossi, Stiel, and Thodos for viscosity has been utilized to develop a generalized correlation for the thermal conductivity of nonpolar substances by the use of the residual relationship for this property and dimensional analysis.Leonard I . Stiel is with Syracuse University, Syracuse, New York. DIMENSIONAL ANALYSISSeveral investigators have suggested that the thermal conductivity in the dense gaseous and liquid regions is dependent on Cp, the heat capacity (10, 12). If th' is variable is included in a dimensional analysis treatment of the residual relationship, the resulting expression would indicate th...

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