Page 171 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

126 Fundamentals of Water Treatment Unit Processes: Physical, Chemical, and Biological

2. For down-flow, from Figure 6.33 5. In other words, the effective area of the plate is the
projection of its area to the horizontal plane. The
v o d=cos u surface overflow velocity, SOR, then is (neglecting
(6:33)
¼
v P (L d tan u) the 1.16d factor)
3. For cross-flow, from Figure 6.34
Q(plate)
v o
A(projection-of-plate-area-on-horizontal-plane)
d=cos u
v o
(6:34) (6:41)
¼
v P w(plate)
The equality is true for up-flow, down-flow, or hori-
where
v P is the mean velocity within plate cell (m=s) zontal-flow plate settler systems, or for tube settlers
v o is the fall velocity of smallest particles to be (usually operated as up-flow).
removed completely (m=s)
L is the length of plate (m) 6.10.1.6.3 Relationship between SOR, HLR(cross
d is the distance of plate separation (m) section), and HLR(horiz plane)
w(plate) is the width of plate assembly (m) Three definitions of unit flows for plate settlers are
3
Q(plate) is the flow per cell between plates (m =s)
1. Surface overflow rate: The SOR is the flow between
6.10.1.6.2 Effective Plate Area for Up-Flow Plate Settlers two plates divided by the area of a single plate
To arrive at the effective plate area, the pattern of Section projected on the horizontal plane:
6.3.3.1 for conventional basins is followed, i.e.,
Q(plate)
1. Modify Equation 6.32 to place cos u in the denom- SOR v o (6:42)
L(plate) cos u w(plate)
inator:

d(plate)= cos u
¼ v P (6:43)
d L(plate)
v o
(6:35)
d
¼
v P
cos u
cos u sin u 2. Hydraulic loading rate based on plate cross section.
L þ
HLR(cross section) is defined as the flow between
d
(6:36) two plates, Q(plate), per unit of cross-sectional area
d
¼
normal to the velocity vector v P :
sin u
L cos u þ
2. Now recall Q(plate)
d(plate) w(plate)
HLR(cross-section) v P
Q(plate) (6:44)
(6:37)
v p ¼
w(plate) d
3. Hydraulic loading rate based on basin area projected
3. Substitute Equation 6.37 in Equation 6.36: to horizontal plane, HLR(horiz-plane),
Q(plate) d
d (6:38) HLR(horiz-plane) v P sin u
w(plate) d
v o ¼
L cos u þ Q(plate)
sin u

[d(plate)=sin u] w(plate)
Q(plate)
(6:39) (6:45)
d
¼
w(plate)
L cos u þ
sin u
The first, i.e., SOR, appears most frequently in the literature
4. The effective area for settling is the denominator. If
and was adopted here. The other two are given for reference.
we let u ¼ 608, then d=sin u ¼ 1.16d, which is small
If SOR is used, its meaning is usually understood, i.e., as
relative to L, can be neglected to give
defined in Equation 6.42. On the other hand, hydraulic-
loading-rate (HLR) is often used without being defined; the
Q(plate) term should be defined, i.e., in terms of cross section normal
(6:40)
L cos u w(plate) to the plate length axis or to the plate separation distance
v o