Batch settling behaviors of various homogeneous flocculated slurries, such as precipitated cal-cium carbonate, clay, and raw Portland cement slurry, were studied and the following conclusions were obtained.
1. The constant k in Roberts' equation (3) or (4), which is applicable to the settling of a slurry without stirring, had been supposed to be independent of both the initial concentration C₀ and initial height H₀ of the slurry. However, it was found to be inversely proportional to the product C₀H₀, which is equal to the mass of solid per unit sectional area of the settling tank. The data for the settling of slurries with various C₀ & H₀, therefore, may be correlated to a single curve by plotting H/C₀H₀ against t'/C₀H₀, where t' is the time after the beginning of the falling rate period, Thus, the equation for the curve is
(9)
With a specific slurry, H_∞/C₀H₀ & H_c/C₀H₀ in equation (9) may be considered approximately constant. This equation is a generalized form of Roberts' equation, and does not contradict the relations proposed by Work-Kohler & Robinson for the reconstruction of settling curve.
2. In batch settling with raking action, the constant rate period is followed by the 1st & 2nd falling rate periods successively, and the 1st falling rate period lasts for a considerably long time. Settling curves for this period may be expressed by the following equation.
(21)
where κ' & n are constants independent of C₀ & H₀, and n is about -0.6 for CaCO₃ slurry.
3. Height versus time curves with some coloured particles which were mixed beforehand with a slurry, are found to be similar to the settling curve of thet slurry. This similarity relation of settl-ing curves provides a method of computing the concentration distribution along the height of the slurry at any time from a single set of settling curve data. A graphic method is shown in Fig. 8 & 9 and the computed results have proved to be in good agreement with the observed values. Concentration distribution in the batch settling with raking action, may be expressed by the follo-wing equation.
(29')
where C' is the concentration at height H' at time t, and κ' and n are constants in the equation (21).

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Graphical methods for predicting pressure-temperature relations of binary azeotropes have been suggested in the past. Starting with the observation that the logarithum of the azeotropic pressure versus 1/(t+230) yields a straight line plot for binary systems, thermodynamical equation have been developed which relate:
(1) the azeotropic pressure and temperature to the heat of vaporization of one of the com-onents and its liquid phase activity coefficient, and
(2) the liquid phase activity coefficients and compositions of the binary azeotrope to its azeo-tropic temperatures.
As suggested by the thermodynamic derivations the liquid phase activity coefficients of the azeotrope plots as a straight line function when plotted versus 1/T. A method is described for predicting the compositions of the azeotrope at various temperatures from two experimental azeotropic compositions. Tables and figures are presented to illustrate the application of this thermodynamic nalysis.

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Performance characteristics of a liquid cyclone as a hydraulic classifier were examined with various cyclones having 3-6″ diameters, and their dimensions were shown in Tables 1, 2 and Fig. 2.
Tangential velocity distribution, pressure drop, flow ratio, fractional recovery curve and 50% recovery particle size were measured under the various operating conditions.
i) Velocity distribution. Two zones were observed in the cyclone as shown in Fig. 5. The one is the outer zone near the cyclone wall where the tangential velocity is approximately constant, and the other is the inner zone where the velocity distribution is represented by the equation urn=const, in which n equals approximately 0.8 with dilute slurry. Tangential velocity in the cyclone may be correlated with inlet velocity us by the equations (1)-(4).
ii) Pressure drop through cyclones with various proportions may be represented by the experimental equation (7), which agrees fairly well with the theoretical equation (12) calculated from the velocity distribution.
iii) Flow ratio depends primarily on the ratio D_u/D_e and the feed pressure. As the pressure increases, the flow ratio decreases asymptotically to its minimum value which may be estimated by Oyama's equation (14) as a function of D_u/D_e.
iv) Classifying charateristics of liquid cyclone may be represented by the fractional recovery versus particle size curves. These curves with different flow ratios and operating conditions, differ from each other, but may be correlated to a single curve by correcting the flow ratio to zero through the procedure shown in Fig. 12 and equation (15), and plotting those reduced recovery values with d/d₅₀' as shown in Fig. 13 where d₅₀' is a 50% particle size in the reduced recovery curve.
v) Standard proportion. The liquid cyclone having the proportion of D_i/D_c=1/7, D_e/D_c=1/5 is recommended by the authors as a standard, whose capacity, pressure drop and the d₅₀' values are shown diagramatically in Fig. 16, where the density of the solid particle is assumed to be 2.6 and the liquid is water at ordinary temperature.

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