Page 401 - Water and wastewater engineering
P. 401

10-18   WATER AND WASTEWATER ENGINEERING

                                 The following theoretical development is from MWH (2005). The settling time for a particle
                            to move between countercurrent parallel plates is
                                                                      d
                                                              t                                        (10-23)
                                                                   v s cos
                             where     t       settling time, s
                                      d       distance between two parallel plates (as shown in  Figure 10-12 ), m
                                      v    s        particle settling velocity, m/s
                                             inclination angle of plates from horizontal, degrees
                             If a uniform velocity is assumed, then the particle travel time spent in the plates is

                                                                      L p
                                                           t p                                         (10-24)
                                                                 v fc    v s sin

                             where  t    p         particle travel time spent in plates, s

                                     L    p         length of plate, m
                                      v    fc        fluid velocity in channel, m/s
                                 If the trajectory of a particle that is shown in  Figure 10-12  is considered, then all of the par-
                            ticles with a settling velocity  v    s    are removed. If  Equation 10-23  is equated to  Equation 10-24 ,  t    p    is
                            equal to the settling time  t.  Those particles with a larger settling velocity are also removed, that is
                                                                     v fc  d
                                                        v s                                            (10-25)
                                                               L p cos       d sin

                                 The fluid velocity,  v    fc   , may be determined from the number of channels
                                                                      Q
                                                               v fc                                    (10-26)
                                                                     Ndw

                                                3
                             where  Q      flow rate, m  /s

                                      N      number of channels, dimensionless
                                      w      width of channel, m
                                 If one assumes that the surface area of the basin is comprised of plates and that the area occu-
                            pied by the plates is ignored, then the fluid velocity,  v    fc   , is also related to the overflow rate of the
                            basin
                                                                 Q        Q
                                                          v fc                                         (10-27)
                                                                Ndw     A sin
                                                      2
                             where  A      top area of basin, m .
                                 Depending on where they enter the plate, particles with settling velocities less than  v    s    may
                            also be removed.
   396   397   398   399   400   401   402   403   404   405   406