During a study to determine mixing intensity, four groups of jars-test systems were utilized and mean velocity gradient, turbulent gross drag coefficient, and Reynolds and Power numbers were calculated. It was concluded that the same G, or mean velocity gradient, values could be produced by impellers of different shapes as long as projected areas were the same.The jar-test procedure is widely used to simulate the water-pretreatment process in the laboratory to produce data for process control, yet few carefully controlled jar-test techniques are found in related literature. Jar-testing has depended upon the approach of each investigator. 1 "3 However, the interpretation of jar-test data must be founded on unvarying and well-calibrated techniques if they are to be quantitatively meaningful. One of the important variables in the procedure is the mixing intensity, which is related to the rotational speed and the configuration of the agitator as well as the geometry of the mixing vessel.The purpose of this study was to determine the mixing intensity, expressed as the mean velocity gradient "G," throughout the applicable speed range, using various jar-test configurations. The resulting data should prove useful for appli- OCTOBER 1975 cation of laboratory data to water-treatment-plant design.Camp' has called attention to the facts that (1) the fluid condition in full-scale plant mixing and flocculation basins is always turbulent, even when G values are relatively low; and (2) at speeds commonly used in jar-test machines, laminar flow conditions may occur. One object of this study was to evaluate the minimum threshold speeds above which turbulence always occurs in jar-testing.Camp and Stein5 applied Stokes' theory" to relate the total energy input to what they called a root-mean-square velocity gradient G (Stokes' theory states that the velocity gradient equals the square root of energy dissipation at a point, divided by the absolute viscosity of the fluid):,where W = dissipation function = power loss per unit volume of fluid ju = absolute viscosity of the fluid The value of W depends upon the geometry of the stators, rotors, and containers and upon the speed of the rotors. Accurate values of W can be determined best by measurement of the torque input to the liquid at various speeds and temperature:in which j is the measured rotor speed in rps, T is the measured torque input, and V is the liquid volume. Once the torque is determined, the value of W can be calculated.By extensive experiments with hydrous ferric oxide floe, Camp 7 demonstrated that the floe size and volume concentration may be R. J. LAI ET AL 553
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