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re PD: = - EXAMPLE 3.4 (Solid dissolution in an agitated vessel) A solution of K Cr20, is to be prepared by dissolving crystals of the solid in an agitated vessel. Twenty kilograms of the solid is charged into a vessel containing 500 kg water. The vessel is provided with a flat-bladed turbine that rotates at 120 rpm. Following data are given: density of the solid = 2690 kg/m; average particle size = 0.6 mm; solubility of the solid in water at the given temperature = 8 wt%; average viscosity of the solution over the concentration range involved = 0.98 cP; density of the liquid = 1000 kg/m (assumed constant); diffusivity of potassium dichromate in water = 1.5 x 10-3 cms. Calculate the time required for complete dissolution of the solid. The following correlation for Sherwood number can be used to calculate the solid-liquid mass transfer coefficient. kzd, Sh = = 2 + 0.44(Re)0.504 (Sc)0.355 D where Nd p. Res = stirrer Reynolds number ; Sc = 5; dp = particle diameter. u Hints: Let at any time t, the mass of the undissolved solid in the vessel be m kg. Mass of solid already dissolved = 20 m. Mass of solution = 500 + (20 m), volume = (520 - m)/1000 m. Instantaneous concentration of the solution, C = (20 m)/[(520 m)/1000] kg/m. Solubility, C = 80 kg/m Now we express the quantities ku and a (the total area of the particles at the time, t) in terms of m. If do = 0.6 mm (the initial diameter of a particle), the number of particles = 6.574 x 10" Mass of a single particle at the time t = m/(6.574 x 10'); instantaneous diameter, dp = 2.211 x 10(m) 3, area of a particle = ade2 = ()[2.211 x 10-4(m)1/3)*; total area of the particles, a = (10.1)m23. Schmidt number, Sc = upD = 653. 22to0 cm Instantaneous Reynolds number, Res = (0.09976)(m)2/3 kid, Sh = 2 + (0.44)(0.09976 x m2/3)0.504(653)0.385 = 2 + 1.67m D ku = (6.784 x 10-)(2 + 1.67m0.336)(m)-1 The rate of dissolution of the crystals can be written as dm kua(C, - C) dt 0 90 (20 - m)(1000) [(6.784 x 10-)(2 + 1.67m0.336)m-1/3)(10.1m213) 80- = o(m) Numerical integration of the above equation (from m = 20 to m = 0) gives the time of dissolution.. Ans. 15 min Nd PVD 70.336 -1/3 uppfost 0.3% 20x200 Dr. 20 -1/3 ( 80 520 - m EDMI NOTE 8 P AI QUAD CAMS