Page 411 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

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

2
v(superficial) (gpm/ft ) and
0 5 10 15 20 25 30 35 40
600
rv mf d 60
(12:52)
R ¼
m
500
1.6
15°C Bed is fluidized The second part of the protocol is to determine the bed
400 30°C 1.2 expansion for v v mf , which may be done by two empirical
Δh (mm) 300 Δh (ft) relations (Amirtharajah and Cleasby, 1972; Cleasby and Fan,
1981, p. 460), that is,
200 0.8 4:7 1:687
e Ga ¼ 18R þ 2:7R (12:53)
0.4
100
Coarse sand, d =1.03 mm and
60
20 in bed depth
0 0 3 2
d r (SG s 1)g
0 20 40 60 80 100 30 w (12:54a)
m
Ga ¼ 2
v(superficial) (m/h)
3
2
d r (SG s 1)g
60 w
FIGURE 12.34 Headloss versus backwash velocity. (Adapted Ga ¼ (12:54b)
m 2
from Amirtharajah, A. and Cleasby, J.L., J. Am. Water Works
Assoc., 64(1), 56, 1972.)
where Ga is the Galileo number (dimensionless).
where The bed expansion is
v mf is the backwash velocity for incipient fluidization (m=s)
(h h o ) (e e o )
d 60 is the media size that is 60% finer than (mm) ¼ (12:55)
h o (1 e)
SG(medium) is the specific gravity of medium
2
m is the dynamic viscosity of water (N s=m ) The calculation protocol that applies to Equations 12.50
through 12.55 is embedded in Table CD12.7, which was
Converted to U.S. Customary units, the coefficient is, formatted to calculate the expanded bed depth as a function
3.81 10 3 (instead of 3.22 10 11 ); the exponents are the of assumed superficial backwash velocities. In other words,
same for both systems of units. the calculation protocol assumes a v, which permits calcula-
tion of R by Equation 12.52. At the same time Ga is calcu-
12.4.4.6.4 Bed Expansion Calculation Protocol
lated by Equation 12.54. Then e 4.7 is calculated from Equation
Equation 12.50 for v mf is valid for R 10. For 10 < R < 300, a
12.53. The minimum fluidization velocity, v mf , is calculated
by Equation 12.50 with correction by Equation 12.51 incorp-
correction factor K R is applied to v mf , that is, v mf (corrected) ¼
K R v mf , and is calculated as
orated (if 10 < R < 300). Calculation of v mf is necessary since
0:272 Equations 12.52 through 12.54 are valid only for v > v mf .
(12:51)
Table CD12.7 may be used to calculate bed expansion versus
K R ¼ 1:775R mf
where an assumed backwash velocity for assumed conditions, for
example, temperature, specific gravity of medium, d 10 , etc.
K R is the correction factor for10 < R < 300, applied to v mf
R mf is the Reynolds number calculated for whatever con- Amirtharajah and Cleasby (1972) showed comparisons
ditions exist when R > 10 between the expanded bed depth calculation, that is, h,by
TABLE CD12.7
Excerpt—Bed Expansion as Function of Backwash Superficial Velocity and Calculation of Minimum Fluidization
Velocity with Correction (Equations from Amirtharajah and Cleasby, 1972)
(a) Calculation of bed expansion by Wen=Yu Equation from Amirtharajah and Cleasby, 1972
g ¼ 9.80665
Data Concerning Media and Conditions
v
T m d 10 d 60 d o r w
3
2
2
(8C) (Ns=m ) (mm) (mm) e o (mm) SG(media) (kg=m ) (m=h) (m=s) (gpm=ft ) Ga R e 4.7 e
20 0.001005264 0.43 0.69 0.412 513 2.648 998.37 2.0 0.00056 0.81833 5237 0.38 0.0014 0.25
20 0.001005264 0.43 0.69 0.412 513 2.648 998.37 4.0 0.00111 1.63666 5237 0.76 0.0029 0.29
22 0.000957291 0.50 0.689 0.407 457 2.655 998.37 6.0 0.00167 2.45499 5770 1.20 0.0044 0.31
22 0.000957291 0.50 0.689 0.407 457 2.655 998.37 8.0 0.00222 3.27332 5770 1.60 0.0060 0.34