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.