Environmental Engineering FOURTH EDITION

Water Treatment 139

From

rapid

mix

Figure 7-4. Flocculator used in water treatment.

p = fluid density (kg/m3 or lb-s2/ft3), and

CD = drag coefficient.

The velocity gradient produced as a result of a power input in a given volume of

water Vis

where

G = velocity gradient (in s-'),

v = viscosity (in dyne-s/cm2 or lb-s/ft2), and

v = tank volume (in m3 or ft3).

Generally accepted design standards require G to be between 30 and 60 s-l.

Time is also an important variable in flocculation, and the term GT is often used

in design, where T is the hydraulic retention time in the flocculation basin. GT values

are typically between lo4 and lo5.

EXAMPLE 7.1. A water treatment plant is designed for 30 million gallons per day (mgd).
The flocculator dimensions are length = 100 ft, width = 50 ft, depth = 16 ft. Revolving
paddles attached to four horizontal shafts rotate at 1.7 rpm. Each shaft supports four
paddles that are 6 in. wide and 48 in. long. Paddles are centered 6 ft from the shaft.
Assume CD = 1.9, and the mean velocity of water is 35% of the paddle velocity. Find
the velocity differential between the paddles and the water. At 5OoF, the density of
water is 1.94 lb-s2/ft3 and the viscosity is 2.73 x lb-s/f?-. Calculate the value of
G and the time of flocculation (hydraulic retention time).