Page 189 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

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

gives H a ¼ 0.76 m (2.50 ft). From Table 7.5, the width of 2.1 Depth of water, d, in grit chamber at Q(max),
the flume at entrance is 1.206 m (3 ft–11 1=2 in.).
1. By trial-and-error determine a suitable width, w, for grit Q( max )
chamber: For each trial, a series of steps are required. The d ¼ w v H
idea is to first calculate the depth, d, of the grit chamber, 3
based upon an assumed width at Q(max). We can also let 0:765 m =s
¼
v H (max) ¼ 0.38 m=s (1.25 ft=s), the maximum permissible 2:74 m 0:381 m
scour velocity. Knowing d, the depth of the grit chamber,
¼ 0:73 m (2:40 ft)
the next step is to ‘‘set’’ the elevation of the flume floor,
which is located a distance H a (max) below the water
surface at Q(max); keep in mind that the grit chamber 2.2 Setting the Floor of the Flume
water surface must be contiguous with that of the Parshall Figure 7.8 shows how the floor of the flume is to be set
flume at all depths. Note that the flow at Q(max) is what relative to the grit chamber. The floor of the grit chamber is
sets the floor of the grit chamber. Next, v H at Q(min) may set at d(max) ¼ 0.73 m (2.40 ft) below the water level. The
be calculated. If v H < 0.23 m=s (0.75 ft=s), an increase in w floor of the flume is H a (max) ¼ 0.67 m (2.19 ft). At the
will result in a higher v H at Q(min). same time, the floor of the flume is, DZ ¼ d(max)
H a ¼ 0.73 0.67 ¼ 0.06 m (2.40 2.19 ¼ 0.21 ft) above
Trial 1 Assume the grit chamber has a width of 1.22 m
(4 ft 0 in.). the floor of the grit chamber.
1.1 Depth of water, d, in grit chamber at Q(max), 2.3 Check v H at Q(min)
. Check horizontal velocity, v H in grit chamber when
Q( max ) Q(min) ¼ 0.425 m =s (15 ft =s).
3
3
d ¼ 3
w v H . From Equation 7.6, Q(min) ¼ 0.425 m =s ¼
1.55
3
0:765 m =s 1.43H a ; H a (min) ¼ 0.457 m.
1:219 m 0:381 m
¼
3
Q( min ) ¼ 15:0ft =s ¼ 8:0H a ( min ) 1:55 ;
¼ 1:65 m (5:40 ft)
H a ( min ) ¼ 1:50 ft:
1.2 Setting the Floor of the Flume
Figure 7.8 shows how the floor of the flume is to be set . Depth in grit chamber: d(min) ¼ H a þ DZ ¼ 0.457 þ
relative to the grit chamber. Thus, with the upstream water 0.06 ¼ 0.52 m (1.50 þ 0.21 ¼ 1.71 ft).
3
surface as the control, the floor of the flume is set at . Therefore, v H (min) ¼ Q(min) ¼ (0.425 m =s)=(2.74 m
H a (max) ¼ 0.67 m (2.19 ft) below the water level. At the 0.52 m) ¼ 0.30 m=s
3
same time, the floor of the flume is 0.98 m (3.21 ft), that is, and in U.S. Customary units, (15 ft =s)=(1.71 9.0) ¼
0.97 ft=s).
DZ ¼ d(max) H a ¼ 1.65 0.67 ¼ 0.98 m (5.40 2.19 ¼
3.21 ft) above the floor of the grit chamber. . The value of v H (min) approaches the v H ¼ 0.30 m=s
(1.0 ft=s) ideal.
1.3 Check v H at Q(min)
. Check horizontal velocity, v H , in grit chamber when
2. Selection: A spreadsheet, following the foregoing
3
3
Q(min) ¼ 0.425 m =s (15 ft =s). protocol, would facilitate further trials that could factor in
3
. From Equation 7.6, Q(min) ¼ 0.425 m =s ¼ other considerations, for example, achieving a long and
1.55
1.43H a ; H a (min) ¼ 0.457 m. narrow grit chamber while, at the same time, maintaining
3 0.23 v H 0.38 m=s (0.75 v H 1.25 ft=s). Of the two
And, in U.S. Customary units, Q(min) ¼ 15.0 ft =s ¼ widths investigated, the w ¼ 2.74 m (9.0 ft), more closely
8.0H a (min) 1.55 ; H a (min) ¼ 1.50 ft.
approximates the ideal than w ¼ 1.22 m (4.0 ft).
. Depth in grit chamber: d(min) ¼ H a (min) þ 3. Length of grit chamber: The settling velocity for a
DZ ¼ 0.457 þ 0.98 ¼ 1.44 m. 0.2 mm quartz sand particle (SG ¼ 2.65, T ¼ 208C) is
v o 25 mm=s (0.08 ft=s) (ASCE-WPCF, 1977, p. 143).
In U.S. Customary units, d(min) ¼ 1.50 þ 3.21 ¼ 4.71 ft.
Also, from preceding calculations, let w(grit chamber) ¼
3
2.74 m (9.0 ft). Then from the relation,
. Therefore, v H ¼ (0.425 m =s)=(1.219 m 1.44 m) ¼
0.24 m=s; which is close enough to the 0.23 lower
limit.
Q(grit chamber) ¼ w(grit chamber) L(grit chamber) v o
3
3
In U.S. Customary units, v H ¼ (15 ft =s)=(4.0 ft 4.71 ft) ¼ 0.425 m =s ¼ (2.74 m) L(grit chamber) (0.025 m=s)
0.80 ft=s.
. Although v H (min)¼ 0.24 m=s (0.80 ft=s) approxi- L(grit chamber) ¼ 6.20 m (20 ft)
mates, closely enough, to v H (min)¼ 0.23 m=s (0.75
ft=s), further trials might yield a more satisfactory result. The length to width ratio is L(grit chamber)=w(grit
chamber) ¼ 6.20 m=2.74 m 2.2, which is marginally
Trial 2 Assume the grit chamber preceding has a width acceptable. Further trials would be in order to search for
of 2.74 m (9 0) . a higher L=w ratio.
00
0