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Science of Water : Concepts and Applications

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<strong>Water</strong> Treatment Calculations 337<br />

For complete mixing:<br />

For plug fl ow:<br />

where<br />

t = detention time <strong>of</strong> the basin, min<br />

V = volume <strong>of</strong> basin, m 3 or ft 3<br />

Q = fl ow rate, m 3 /s or cfs<br />

K = rate constant<br />

C i = infl uent reactant concentration, mg/L<br />

C e = effl uent reactant concentration, mg/L<br />

L = length <strong>of</strong> rectangular basin, m or ft<br />

v = horizontal velocity <strong>of</strong> fl ow, m/s or ft/s<br />

Example 10.22<br />

V 1 C C<br />

t <br />

⎛ ie⎞ Q K ⎝<br />

⎜<br />

C ⎠<br />

⎟<br />

V L C<br />

t <br />

Q v K C<br />

1 ⎛ i ⎞<br />

⎝<br />

⎜<br />

⎠<br />

⎟<br />

Problem:<br />

Alum dosage is 40 mg/L K = 90 per day based on lab tests. Compute the detention times for complete<br />

mixing <strong>and</strong> plug fl ow reactor for 90% reduction.<br />

Solution:<br />

Step 1. Find Ce .<br />

C (1- 0.9) C 0.1C 0.140 mg/L 4mgL e i i<br />

Step 2. Calculate t for complete mixing (using Equation 10.20).<br />

1 1 40 mg/L4mgL t ( Ci - C ) <br />

⎛<br />

⎞<br />

e<br />

k 90d<br />

⎝<br />

⎜ 4 mgL ⎠<br />

⎟<br />

1d<br />

1440 min<br />

9<br />

90 1d<br />

144<br />

min<br />

Step 3. Calculate t for plug fl ow using the following formula.<br />

FLOCCULATION<br />

1 C<br />

t <br />

⎛ i<br />

ln<br />

⎞<br />

K ⎝<br />

⎜<br />

C ⎠<br />

⎟<br />

e<br />

1440<br />

⎛ ln<br />

90 ⎝<br />

⎜<br />

36. 8 min<br />

40<br />

4<br />

e<br />

⎞<br />

⎠<br />

⎟<br />

e<br />

(10.20)<br />

(10.21)<br />

Flocculation follows coagulation in the conventional water treatment process. Flocculation is<br />

the physical process <strong>of</strong> slowly mixing the coagulated water to increase the probability <strong>of</strong> particle

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