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362 Physical•TreatmentProcesses <br />Settling operations may be classified approximately as falling into four <br />separate categories: type I, type Il, zone, and compression, all dependent on the <br />conttntration of the suspension and the character of the particles.l Types I and <br />II clarificetions both deal with dilute susponsions, the diflerence being that qPe I <br />consists oCessentially discrete par'icles �vhile r�pe II deals with flocculent mate- <br />rials. Zont seftling describes a mass•settling proass in intermediataconcentration <br />suspensions of flocculent materials, and romprersion results whes the concentra- <br />tion incrwses to the point where particles are in physical contact with one <br />another and supported partly by the compacting mass. The following section <br />presents theoretical aspects of various types of sedimentation and indicates how <br />this knowledge can be ueed in design. <br />9-10 <br />TYPE 1 SEDIMENTATION <br />Type I udim_ntation is conamed with removal of nonflocculating discrete <br />particles in a dilute snspension. Under such circumstances the settling may be <br />said to be unhindered and a function only of fluid properties and characteristics <br />of the particle. Settling of heavy, inert materials would be an example of type I <br />StdlIDC0I8tlOt1. <br />A discrete particle (one that retains its individual characteristics) placed in a <br />quiescent fluid will acalerate until fluid drag reachos equilibrium with the <br />driving force acting on the particle. At the moment of equilibrium the parucle <br />begins to settle at a uniform velocity. Sina this condirion of equilibrium is <br />rapidly reached for the general conditions encountered in practia, terminal <br />settling velocity is of particular importance in sedimentation studies. <br />The driving force, which is the net efiect ot the particle weight acting doa�n- <br />ward and the buoyant force of the 8uid acting upward, is given by <br />F � (Y, — Y)V <br />wLen F= driving force <br />q„ y= specific weights of the parGcle and fluid, respectively <br />V= volume of the particle <br />(9•15) <br />Ttro drag Corce acting on a particle is a function of the fluid density and viscosity, <br />settling velocity of the particle v„ and a characteristic dimension of the particle d. <br />A dimensionally derived relationship for fluid drag can be shown to take the <br />form <br />FD a Cn�G�: <br />2 <br />where FD = drag force <br />Co = Newron's drag coefficient <br />A= projected area oCthe particle in the direction of motion'� <br />(9-16) <br />cc <br />io <br />FI6URE 8-it Dra9 coefficients lor sph <br />solulion (or tyiinder: curve II: Stokei sol <br />(Source: fl. M. Olson, Essenlisls o/ fnp• <br />Donnelley Publisher, 1967 ). p. 261.] <br />The drag coe(ficient is a function <br />For Reynolds numbers less than <br />betwan 1 and ]0`, CD can be apF <br />Co = 24 + 3 + 034 <br />Re � <br />Equating driving and drag fo� <br />conditions, <br />CD Apv; <br />�Yr — 7)V � Z <br />A rearrangement of this equation <br />ZiY. — Y)V <br />u� CD AP <br />which is the expression for settlin; <br />are assumed to be spherical in sh <br />substitutions and setting y= pg a <br />u— 49P,-'Pd <br />.— 3CD—P <br />