Page 182 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Grit Chambers 137

TABLE CD7.1
Solution for Example 7.1—Shield’s Equation for Scour in Grit Chamber
v c g d v c
2
(m=s) b f (m=s ) SG (m) (m=s)
(a) Scour velocity for 0.2 mm quartz particle:
0.06 0.03 9.81 2.65 0.0002 0.23
(b) Diameter of quartz particle scoured at 0.3 m=s(1 ft=s) and sensitivity to constants, b and f:
0.30 0.06 0.03 9.81 2.65 0.0004
0.30 0.08 0.023 9.81 2.65 0.0002
(c) Size of organic size matter scoured at SG ¼ 1.2 and 1.05:
0.30 0.06 0.03 9.81 1.2 0.003
0.30 0.06 0.03 9.81 1.05 0.012

Source: Londong, J., Water Sci. Technol., 21, 13, 1989.

Example 7.1 Scour Velocity in Grit Chamber cross-sectional area, it follows that A must be a linear function
(Adapted from Camp, 1946) of Q if v H is held constant, that is,

Problem Statement Q ¼ v H A (7:2)
(a) Estimate the highest velocity in a grit chamber to
avoid scour of sand particles 0.2 mm is size. where v H ¼ 0.3 m=s (1.0 ft=s)—a constant. This mathematical
(b) Determine the sand size that will be started in condition can be accomplished by several methods, described
incipient motion if the velocity is 0.3 m=s (1.0 ft=s).
in the following sections.
(c) Determine the size of organic matter (assume
SG ¼ 1.2 and then 1.05) that will be scoured.
(d) Look at any other variations that may be of interest. 7.2.2.1 Proportional Weir
For channels with vertical walls, the width, w, is constant, and
Solution therefore the depth must be a linear function of flow, Q.A
The most expedient means to solve (a), (b), and (c) is by proportional weir, shown in Figure 7.3, has this characteristic,
means of a spreadsheet, that is, Table CD7.1, which is that is, Q ¼ kd. The proportional weir may be dimensioned by
based on the Shield’s equation. Equations 7.3 through 7.5. Terms are defined in Figure 7.3.
Comments To expand further, a proportional weir is a plate that
The Shield’s equation is used to estimate design limits fits across the channel (Figure 7.3). Below the weir, a free
for channel velocity for a horizontal flow grit chamber.
With respect to task (d), once set up, as in Table CD7.1,
the algorithm can be used in a sensitivity analysis to
assess the effect of errors, in choosing b and f and
the effects of varying v c on particle sizes that may be
scoured, etc.
C L

7.2.2 HORIZONTAL VELOCITY CONTROL
As noted in Section 7.2.1.2, the importance of maintaining a
x
constant horizontal flow velocity of 0.3 m=s (1.0 ft=s) has long y h
been understood. The use of two or more parallel channels
will accomplish this; a number of such examples are given in
Metcalf and Eddy (1916). In other words, as flow increases a
above a certain ‘‘set-point,’’ the second grit chamber will b
come into operation. Practice, however, has favored a single
channel having some method for velocity control to maintain FIGURE 7.3 Proportional weir—used with grit chambers to main-
constant v H . Since flow, Q, is the product of v H and A, the tain constant velocity.