S e ¼ S o
1Àp
ð
Þ
À 1 À p
ð
Þk T aV=Q
h
i 1= 1Àp
ð
Þ
½
Š
ð3:57Þ
where S e is the effluent substrate concentration, mg/L; S o is the bulk liquid substrate
concentration, mg/L; p is a coefficient not equal to 1; and Q is the flow rate, cm
3 /d.
7.8 US Army Design Formulas
In 1972, the US Army Corps of Engineers (US ACE) studied water problems in
urban areas in addition to its traditional sanitary science role at recreation sites. Six
years later, new design equations were developed by the US ACE for design of the
plastic media trickling filters [147]. Equations [58] to [60] are presented below for
calculating the filter depth, filter surface area, media volume, and sludge production,
respectively [69]:
D ¼ À
q
n
aK ace
ln
L e þ L e R
L o þ L e R
ð3:58Þ
where D ¼ depth of filter, ft; q ¼ hydraulic loading, gpm/ft
2 ; L e ¼ desired effluent
BOD 5 , mg/L; R ¼ recirculation ratio ¼ Q r /Q; L o ¼ influent BOD 5 , mg/L; a ¼ specific
surface area of the media, ft
2 /ft
3 ; n ¼ media factor, determined from laboratory; and
K ace ¼ reaction rate constant ranging from 0.0015 to 0.003, determined in the
laboratory.
A ¼
10
6 Q
1440q
ð3:59Þ
where A ¼ surface area of the filter, ft
2 , and Q ¼ average daily wastewater flow,
MGD.
V ¼ AD
ð3:60Þ
where V ¼ volume of filter media, ft
3 .
P s ¼ 8:34Q L o F s
ð3:61Þ
where P s ¼ sludge produced, lb/d; L o ¼ influent BOD 5 , mg/L; and F s ¼ sludge
production factor, lb solids/lb BOD 5 . F s value ranges from 0.42 to 0.65 lb solids/lb
BOD 5 .
132
L. K. Wang et al.