Handbook of Civil Engineering Calculations

where G = Mean velocity gradient (s

l

)

P = Power requirement (ft-lb/s) (kW)

fju = Dynamic viscosity (lb-s/ft^2 ) (Pa-s)

V= Volume of mixing tank (ft^3 ) (m^3 )

G is a measure of the mean velocity gradient in the fluid. G values for rapid mixing oper-
ations in wastewater treatment range from 250 to 1,500 s"^1 A value of 1,000 s"^1 will be
used here. For water at 6O^0 F (15.5^0 C), dynamic viscosity is 2.36 x IQ-^5 lb-s/ft^2 (1.13 x
10~^3 Pa-s). Therefore, the required power for mixing is computed as follows:

P = G^2 IJiV= (1,000 s~^1 )^2 (2.36 x 10-^5 Ib-s/ft^2 )(24 ft^3 ) = 566 ft-lb/s

= 1.03 horsepower (0.77 kW)

Use the next largest motor size available = 1.5 horsepower (1.12 kW). Therefore, a 1.5

horsepower (1.12 kW) mixer should be used.

3. Determine the required volume and power input for flocculation
   The purpose of flocculation is to form aggregates, or floes, from finely divided matter.
   The larger floes allow a greater solids removal in the subsequent filtration process. In the
   direct filtration process, the wastewater is completely mixed with a polymer coagulant in
   the rapid mix basin. Following rapid mix, the flocculation tanks gently agitate the waste-
   water so that large "floes" form with the help of the polymer coagulant. As in the rapid
   mix basins, mechanical flocculators will be utilized.
   For flocculation in a direct filtration process, the hydraulic retention time will range
   from 2 to 10 minutes. A retention time of 8 minutes will be used here. Therefore, the re-
   quired volume of the flocculation basin is

F= (Sn 1 In)(I x 1O^ gal/day) =al?43ft2l

l,440mm/d

G values for flocculation in a direct filtration process range from 20 to 100 s"^1. A value of

80 s"^1 will be used here. Therefore, the power required for flocculation is

P = G^2 VV= (80 s~^1 )^2 (2.36 x 10-^5 )(743 ft^3 )

= 112 ft-lb/s = 0.2 horsepower (0.15 kW)

Use the next largest motor size available = 0.5 horsepower (0.37 kW). Therefore, a 0.5

horsepower (0.37 kW) flocculator should be used.

It is common practice to taper the energy input to flocculation basins so that floes ini-

tially formed will not be Broken as they leave the flocculation facilities. In the above ex-

ample, this may be accomplished by providing a second flocculation basin in series with

the first. The power input to the second basin is calculated using a lower G value (such as

50 s"^1 ) and hence provides a gentler agitation.

Related Calculations. If the flows to the rapid mix and flocculation basin vary

significantly, or turn down capability is desired, a variable speed drive should be provided

for each mixer and flocculator. The variable speed drive should be controlled via an out-

put signal from a flow meter immediately upstream of each respective basin.

It should be noted that the above analysis provides only approximate values for mixer

and flocculator sizes. Mixing is in general a "black art," and a mixing manufacturer is

usually consulted regarding the best type and size of mixer or flocculator for a particular

application.