Page 450 - Civil Engineering Formulas

376 CHAPTER THIRTEEN

Adjustment for depth. The treatability constant is then adjusted from the
standard depth of 20 ft (6.1 m) to the example filter depth of 25 ft (7.6 m) using
the following equation:
k 30/25 k 30/20 (D 1 /D 2 ) x (13.62)

where k treatability constant at 30°C (86°F) and 25 ft (7.6 m) filter depth
30/25
(as example value)
k treatability constant at 30°C (86°F) and 20 ft (6.1 m) filter depth
30/20
D depth of reference filter (20 ft) (6.1 m)
1
D depth of actual filter (25 ft) (7.6 m) (as example value)
2
x empirical constant (0.3 for plastic medium filters)
The empirical formula used for sizing plastic media trickling filters is
S e n
exp[ kD(Q v ) ] (13.63)
S i
where S BOD of settled effluent from trickling filter (mg/L)
5
e
S BOD of influent wastewater to trickling filter (mg/L)
i
5
k treatability constant adjusted for wastewater temperature and filter
20
depth (k 30/25 )
D depth of filter (ft)
Q volumetric flowrate applied per unit of filter area (gal/min sq ft)
v
2
(L/s m ) Q/A
Q flowrate applied to filter without recirculation (gal/min)(L/s)
2
A area of filter (sq ft) (m )
n empirical constant (usually 0.5)
Rearranging and solving for the trickling filter area (A):
ln(S e /S i 1/n
A Q (13.64)
(k 30/25 )D
2
2
The hydraulic loading of the filter in gpm/ft , or L/s m is
Hydraulic loading Q/A (13.65)
For plastic media trickling filters, the hydraulic loading ranges from 0.2 to
2
1.20 gal/min sq ft (0.14 to 0.82 L/s m ).
The organic loading to the trickling filter is calculated by dividing the BOD
5
load to the filter by the filter volume as follows:
Organic loading BOD /(A) (filter length, ft) (13.66)
5
For plastic media trickling filters, the organic loading ranges from 30 to
2
3
3
200 lb/10 ft d (146.6 to 977.4 kg/m d).
To optimize the treatment performance of a trickling filter, there should be a
continual and uniform growth of biomass and sloughing of excess biomass; to