Page 218 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Flotation 173

TABLE 8.1
Parameter Values in Flotation
Parameter Definition Value
Attachment coefficient a pb ! 1.0 with effective coagulation
a pb
Diameter of floc particle 10 < d b < 100 mm, with median 40 mm; A strong floc of size range 10 d p 30 mm is a goal of
d p
flocculation (Edzwald, 1995, p. 20), which may be controlled by a low alum dosage and flocculation
1
intensity e.g., G 70 s , and duration, e.g., 5–10 min.
Diameter of bubble 40 < d p < 80 mm, with median 50 mm; a size range 20 d b 40 mm is a goal
d b
5
3
Bubble density 10 < N b < 2.4 10 bubbles=mL
N b
5
5
N p Particle density 10 < N p (reaction zone) < 10 particles=mL
Ratio of bubbles to particles N b 10 N p ; B ¼ N b =N p ratio
B ¼ N b =N p
r p Mass density of particles 1010 kg=m 3
3
Mass density of water 998.2063 kg=m at 208C, Table B.9
r w
3
r air Mass density of air at STP 1.2038 kg=m at 208C, Table B.7
The mass density of air may be calculated by the ideal gas law, i.e., PV ¼ nRT. Rearranging gives the molar
density, i.e., n=V ¼ P=RT. Mass density is r(air) ¼ (P=RT) MW(gas)=1000 ¼ 101,325 Pa=(8.31451 Nm=K
3
mol 293.15 K) (28.9641 g=mol=1000 kg=mol); r(mass) ¼ 1.204 kg air=m gas.
2
g Acceleration of gravity 9.8066 m=s , Appendix QR
2
m Dynamic viscosity of water 1.002 10 3 Nm=s , Table B.9
References: Rows 1–7 from Edzwald (1995, p. 12); Rows 8–11 from Appendix B.
STP is an acronym for ‘‘standard temperature and pressure.’’
in which in which d pb is the diameter of the particle–bubble
r pb is the density of the particle–bubble agglomerate agglomerate (m)
3
(kg=m ) 3. The rise velocity, v pb , by Stoke’s law is
3
r p is the density of particles (1010 kg=m ); from
Edzwald (1995, p. 14) g(r r )d 2
w pb pb
d p is the diameter of floc particle (m) v pb ¼ 18m (8:13)
B is the number of attached bubbles (bubbles per
particle)
v pb isthevelocityofparticle–bubbleagglomerate(m=s).
2. Determine the equivalent spherical diameter, d pb :
Table CD8.2 gives results of computations to obtain v pb
h i 1=3 for various particle diameters, d p , for 1, 2, and 10 bubbles
3
d pb ¼ d þ Bd 3 b (8:12)
p
attached per particle based upon Equations 8.11 through 8.13,
TABLE CD8.2
Particle Rise Velocities as Function of Number of Bubbles Attached, B a,b
B n (n ¼ 1) B n (n ¼ 2) B n (n ¼ 10)
d p (mm) r pb (g=mL) d pb (mm) v pb (m=h) r pb (g=mL) d pb (mm) v pb (m=h) r pb (g=mL) d pb (mm) v pb (m=h)

10 0.02 40 3.1 0.01 50 5.0 0.003 86 14.5
20 0.11 42 3.0 0.06 51 4.9 0.01 87 14.5
50 0.67 57 2.1 0.20 63 3.9 0.17 92 13.7
100 0.95 102 1.0 0.90 104 2.2 0.62 118 10.4
200 1.01 200 0 0.99 201 0.3 0.94 205 5.2
500 1.01 500 0 1.01 500 0 1.01 501 0
a
From Table 3, Edzwald, 1995 (reconstructed by spreadsheet computations, Table CD8.2)
b
Computations are based on Equations (8.11) ), (8.12), and (8.13) where
d b ¼ 40 mm
d p ¼ 50 mm
T ¼ 208C, and initial
3 3
r p ¼ 1.01 g=cm [ ¼ 1010 kg=m ]