Solutions to Activated Sludge Math
The flow through an activated sludge plant in 15 mgd. The BOD of the primary effluent is 110 mg/L and the BOD of the final effluent is 8 mg/L. The rate of air flow to the aeration tank is 2,000 cfm. The MLSS is the aeration tank is 2,500 mg/L. The 30-minute settleable solids test is 225 mL/L. The TSS of the primary effluent is 115 mg/L and the TSS of the final effluent is 12 mg/L. The return sludge ratio is 20%. 60,000 gallons of 2% sludge are wasted each day. The flow is split evenly between two rectangular aeration tanks. All tanks are the same size. Each tank is 175 feet long, 75 feet wide, and 12 feet deep.
1.
The perimeter of one aeration tank is ________ feet.
175
ft + 75 ft + 175 ft +75 ft = 500 ft
2.
The surface
area of one aeration tank is ________ square feet.
175 ft x 75 ft = 13,125 sf
3.
The volume of one aeration tank is ________ cubic feet.
175
ft x 75 ft x 12 ft = 157,500 cf
4.
The volume of one aeration tank is ________ 1000-cubic feet.
157,500 cf/1000 = 157.5 1000-cf
5.
The total volume of both aeration tanks together is ________ cubic feet.
157,500
cf x 2 = 315,000 cf
6.
The total
volume of both aeration tanks together is ________ 1000-cubic feet.
315,000
cf/1000 = 315 1000-cf
7.
One aeration
tank holds ______ gallons.
157,500
cf x 7.48 gal/cf = 1,178,100 gal
8.
One aeration tank holds ______
million gallons.
1,178,100 gal/1,000,000 = 1.18
MG
9.
The two aeration tanks together hold
______ gallons.
1,178,100
gal x 2 = 2,356,200 gal
10.
The two aeration tanks together hold is ______ million gallons.
1.18
MG x 2 = 2.36 MG
11.
The return sludge flow is ________ mgd.
20%/100
= 0.2
0.2
x 15 mgd = 3 mgd
12.
The applied flow to the aeration tanks is ________ mgd.
15
mgd + 3 mgd = 18 mgd
13.
The applied flow to one aeration tank is ________ mgd.
18
mgd/2 = 9 mgd
14.
The applied flow to one aeration tank is ________ gpd.
9
mgd/1,000,000 = 9,000,000
gpd
15.
The detention time is ________ hrs.
(1,178,100 gal)
x 24 hrs/day = 0.1309 days x 24
hrs/day = 3.14 hrs
9,000,000
gpd
16.
The total organic load to both aeration tanks is ________ lbs BOD/day.
110
mg/L x 8.34 lbs/gal x 15 mgd = 13,761 lbs
BOD/day
17.
The organic load to one aeration tank is ________ lbs BOD/day.
6,881 lbs BOD/day/2 = 6,881 lbs BOD/day
18.
The organic loading rate on one aeration tank is ________ lbs BOD/day/1000-cf.
3,440
lbs BOD/day/157.5 1000-cf = 21.8 lbs BOD/day/1000-cf
19.
The MLSS in one aeration tank is ________
lbs MLSS.
2,500
mg/L x 8.34 lbs/gal x 1.18 mgd = 24,603
lbs MLSS
20.
The total MLSS in both aeration tanks is ________
lbs MLSS.
2,500
mg/L x 8.34 lbs/gal x 2.36 mgd = 49,206
lbs MLSS
21.
The F/M is ________.
6,881
lbs BOD/24,603 lbs MLSS = 0.28
22.
The total amount of sludge wasted daily is ________ lbs WAS/day.
20%/100
= 0.02
60,000
gal x 8.34 lbs/gal x 0.02 = 10,008
lbs/day
23.
The amount of sludge wasted from each aeration tank is ________ lbs
WAS/day.
(10,008
lbs WAS/day)/2 = 5,004 lbs/day
24.
The SRT is ________ days.
(24,603
lbs MLSS)/5,004 lbs/day = 4.92 days
25.
The effluent TSS is ________ lbs
TSS/day.
12
mg/L x 8.34 lbs/gal x 7.5 mgd = 751
lbs/day
26.
The MCRT is ________ days.
24,603 lbs MLSS
= 24,603 lbs MLSS/5,755 lbs/day = 4.28
days
(5,004 lbs/day + 751 lbs/day)
27.
The influent TSS is ________ lbs TSS/day.
115
mg/L x 8.34 lbs/gal x 7.5 mgd = 7,193
lbs/day
28. The sludge age is ________ days.
24,603
lbs MLSS/7,193 lbs/day = 3.42 days
29.
The SVI is ________.
225 mL/L x 10,000 = 2,250,000 = 900
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