Page 196 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Grit Chambers 151

The grit remaining after the first compartment is designated
Circulation R(n ¼ 1) and is, (1 P), that is,

R(n ¼ 1) ¼ (1 P) (7:18)
Baffle
The grit remaining after the second compartment, n ¼ 2, des-
ignated as R(n ¼ 2), will be (1 P)(1 P), that is,

R(n ¼ 2) ¼ (1 P)(1 P) (7:19)
¼ (1 P) 2 (7:20)
Diffuser
header
Thus, the general equation for fraction of grit remaining after
n compartments is,
Separation zone
Grit n
Organics Grit collection R ¼ (1 P) (7:21)
Air bubble
(scraper blades not shown)
where
FIGURE 7.13 Elements of an aerated grit chamber. (Adapted from R is the fraction of grit remaining after n passes
USFilter Envirex Products Brochure, c. 1980 now WSG & Solutions. P is the fraction of grit removed after one pass
With permission). n is the number of ‘‘rotation compartments’’ in the length
of the grit chamber, or the number of rotations of the
water mass in length, L
7.3.2.2 Calculation of Spiral Length, DL
Figure 7.16 depicts an ‘‘unfolded’’ spiral (top view), where a
Grit particle
particle starts at A and ends at B, as in Figure 7.15. The length
v T of advance, along the axis of the grit chamber, due to a
rotation is DL over a rotation distance is approximately, pD.
The circulation velocity, v R , has components v T and v H . From
Figure 7.16, the two triangles, shown by different shades, are
v S v R similar, that is,

FIGURE 7.14 Schematic of separation zone in aerated grit cham- DL v H
(7:22)
ber (drawing is in vertical plane). The resultant vector for a given pD ¼ v T
particle is v R (particle) ¼ v S þ v H þ v T .
where
DL is the length of a ‘‘compartment’’ of the grit chamber,
defined as the axial length of the grit chamber for one
rotation of the spiral flow (m)
w
D is the depth of water in the grit chamber, that is, from the
water surface to the top plane of the grit collector (m)
v T
v H is the velocity component of spiral flow in the axial
v H direction (m=s); Q=A(cross section)
v T is the velocity component of spiral flow tangent to the
D A 10 particles at start spiral circulation path in the plane of the grit chamber
of “pass”
cross section (m=s); 0.3 m=s
B
8 particles at end
of “pass” 7.3.2.3 Empirical Guidelines
From empirical guidelines: w=D 0.8; 3 D 5 m (10–15 ft);
scour velocity is, 0.2 v T 0.3 m=s (0.75–1.0 ft=s); and
2 particles deposited;
ΔL
i.e., P =0.2 from continuity, v H ¼ Q=(wD). Thus, DL can be calculated by
Grit collector Equation 7.22.
FIGURE 7.15 Spiral rotation of grit particles showing axial vel- 7.3.2.4 n Determination
ocity vector, v H , and tangential velocity vector, v T ; the particles also
The length of the grit chamber can be calculated as
settle with velocity, v S . Ten particles start at A, two are deposited in
the grit collector, and eight appear at the corresponding position, B.
L ¼ n DL (7:23)
The length of the spiral from A to B is DL.