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284 <br />Type•1 Settlfng <br />The settling of discrete, nonflocculating particles can be aunlyzed bp <br />means of the classic la�cs of sedimentation formulated by \e�cton and <br />Stokes. ATe�cton's !nw �•ields the terminal particle velocit�• by equating <br />the eRective n•eight of the particle to the frictional resistance, or drag. <br />The eliective n•eight is simply�: <br />1V = �P. — P�9V �5�10� <br />��•here p, = density of particle <br />p = density of fluid <br />g= acceleration due to gravity <br />V = volume of particle <br />The drag per unit area depends on the particle ��elocity, fluid densitp, <br />fluid viecosity, and particle diameter. The drag coefficient Cn (dimen- <br />sionless) is de'�ed by Eq. 8•11. <br />Cn = Fa (S•11) <br />�PU�% .i <br />2 <br />�chere F'a = drag force <br />u = patticle velocity <br />.4 = cross-sectionnl or projected aren of particle at right angles <br />to u <br />Equating the drag force to the effective ���eight of the pnrticle, for <br />spherical particles, }•ields \'e�cton's la�c: <br />V� � r4 9ia� — a)d�� <br />�3 Cnv <br />�°I� <br />p <br />u <br />� <br />V <br />0 <br />3 <br />w <br />0 <br />O.00D1 0.01 <br />R� <br />For Reynolds numbers <br />dominates, nnd substiti <br />Stokes' ]a�c: <br />VL = 9�P� - P�d� <br />isµ <br />For laminar flo�c condit <br />Fe = 3xµid <br />Equating this force to tl <br />In the design of se <br />select a particle �cith a t <br />that all particles thnt he <br />V, «ill be removed. Th <br />then <br />(s•I') � <br />Q = .4 V� <br />n•here V, = terminal velocity of particle <br />d = diameter of particle <br />The drag coefficient takes on diHerent 1�nlues depending on <br />�chether the flo�e regime surrounding the particle is laminar or turbu- <br />lent. The drag coetficient is sho�cn in Fig. S•� as a function of the <br />Reynolds number. Although particle shape aSects the value of the <br />drag coefficient, for spherical particles the curve in Fig. S•4 is approai- <br />mnted by the follo��ing equation (upper limit of ATx = 10') [9]: <br />CD = T R -t- �NR } 0.34 <br />Wastewater Engineering: Collection, Treatment, Disposal <br />(3•13) <br />��•here d is the surtace � <br />. yields <br />V, = e = overAos <br />� s=` �chich sha�cs that the o� <br />basis af design, ia equi <br />- also indicates thut for t. <br />�=�: of the depth. <br />�a For continuous-flo• <br />'�1's the time a unit �•olume <br />