Page 197 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

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

v T
A
“Unfolded” spiral circulation path v R
ΔL v H

B
πD

FIGURE 7.16 Spiral circulation path is shown ‘‘unfolded’’ to illustrate relations, that is, DL=pD ¼ v H =v T (by similar triangles).

Three methods to estimate n are: grit particles and from 0.2 v T 0.3 m=s (0.75–1.0
ft=s) (Camp, 1942; Londong, 1989). The value of v T
1. Operating grit chamber: For a design similar to one may be controlled by adjusting the airflow, that is,
being contemplated, suppose R is measured (by Q(air).
laborious effort) along with L. Then DL may be 4. Determine DL: With D, v H , and v T determined, cal-
calculated by Equation 7.22, that is, DL=pD ¼ v H =v T , culate DL by Equation 7.22, that is, DL=pD ¼ v H =v T .
and n by Equation 7.23, that is, L ¼ n DL. From this 5. Determine n: Estimate or assume an n (or a series on
value of n, P can be calculated by Equation 7.21, that n values in a spreadsheet) by one of the three
n
is, R ¼ (1 P) . The grit chamber to be designed methods summarized in Section 7.3.2.4.
would have a similar P, and therefore with a speci- 6. Determine L: Calculate L by Equation 7.23, that is,
fied performance, n can be calculated again using L ¼ n DL. This is an estimate and should be calcu-
Equation 7.21. lated on a spreadsheet so that the variation in the
2. Impute a P: A second approach is to assume a P, say estimate of L can be taken into account. After review
P ¼ 0.2, specify an R, and calculate n from Equation of the spreadsheet, L is selected as a ‘‘decision’’
n
7.21, that is, R ¼ (1 P) . This is best done by a based on judgment.
spreadsheet in which, for a given R, different P’s can 7. Operation—Effect of Increased Flow on R: Suppose
be assumed and systematically changed. Then that the flow for a given plant is increased. From this
another R is assumed and the process is repeated. a new DL can be calculated from Equation 7.22, that
The value of n is determined for each (R, P) pair by is, DL=pD ¼ v H =v T and a new n follows from Equa-
Equation 7.21. From these calculations, the uncer- tion 7.23, that is, L ¼ n DL. Therefore, using the P
tainties can be estimated and the variation in n can be as determined previously, the new R can be esti-
n
assessed. Then DL and L can be estimated by Equa- mated by Equation 7.21, that is, R ¼ (1 P) .In
tion 7.22, that is, DL=pD ¼ v H =v T , and Equation other words, once a design is determined, then the
7.23, that is, L ¼ n DL, respectively. effects of different flow ‘‘scenarios’’ can be assessed
3. Set L and calculate n: Select a value for L and (again, by spreadsheet).
calculate n from Equation 7.23, that is, L ¼ n DL,
with DL from Equation 7.22, that is, DL=pD ¼
v H =v T . From the n so calculated, and an assumed R, Example 7.7 Aerated Grit Chamber Design
n
calculate P by Equation 7.21, that is, R ¼ (1 P) .
Use this P to determine a new n for any specified R, This example problem illustrates the application of the
and thus calculate L by Equation 7.23, that is, equations developed in the rational design of an aerated
grit chamber.
L ¼ n DL.
Problem statement
7.3.2.5 Algorithm for Calculations (a) For an aerated grit chamber with flow, Q ¼ 0.75
3
The forgoing procedure may be summarized as an ‘‘algo- m =s (17.1 mgd), sketch a cross-section view and a
plan view, showing dimensions.
rithm.’’ The algorithm can be applied best as a spreadsheet
(b) Show the air diffuser system and estimate the air-
procedure:
flow.
(c) Document the criteria that you choose.
1. Determine w and D: Assume both w and D from
(d) Suggest alternative criteria.
empirical guidelines, for example, let w ¼ D 3–5m.
2. Determine v H : Knowing Q and having assumed w Criteria: The design criteria could be from either Morales
and D, calculate v H (i.e., v H ¼ Q=(wD). and Reinhart (1984) or Londong (1987, 1989). The criteria
3. Determine v T : From Camp’s criterion for scour vel- from the former are based upon practice as distilled from
ocity for organic matter and for deposit of 0.2 mm their study of grit chambers at five plants. The criteria from