WEF Collection System Practice Exam – Math Questions
1. X (Unknown) = Volume, gals
a. Find the volume of the wet well in Ft3 and then convert to gallons.
Vol. Ft3 = [0.785 x (D, ft.)2] x Depth, ft.
Vol. Ft3 = [0.785 x (13 ft.)2] x 20 ft.
Vol. Ft3 = [0..785 x (13 ft. x 13 ft.)] x 20 ft.
Vol. Ft3 = [0.785 x 169 ft2] x 20 ft.
Vol. ft3 = 132.665 ft2 x 20 ft.
Vol. Ft3 = 2653.3 Ft3
b. Convert cubic foot volume to gallons.
Capacity, gals. = # Ft3 x 7.48 gal./ft3
= 2653.3 ft3 x 7.48 gal/ft3
Capacity, gals. = 1,9846.7 gallons
2. X (Unknown) = GPD wastewater used per person
a. Data:
Population = 65,000 persons (a capital is one person)
Flow = 6 mgd
b. Formula:
GPD/cap. = Flow, GPD
# of persons (cap)
c. Convert 6 mgd to GPD
GPD = 6 MGD x 1,000,000 gals./MG
GPD = 6,000,0000 gal/day
d. Solve the problem:
GPD/cap = 6,000,000 gals/day
65,000 persons
GPD/cap = 92.31 gals./capital
3. X (Unknown) = Flow conversion to MGD
a. Convert 2500 gpm to gpd to mgd
gal/day = 2500 gal/min. x 1440 min./day
gal/day = 3,600,000 gal/day
MGD = 3,600,000 gal/day
1,000,000 gal/Mg
MGD = 3.6 MGD
4. X (Unknown) = Volume of wastewater in pipe in gallons
!1
a. Change 12 inch diameter to ft.
Ft. = 12 inches
12 inches/ft.
Ft. = 1.0 ft.
b. Find volume of pipe in Ft3 then convert to gallons
Volume, ft3 = [0.785 x (D, ft.)2] x Pipe Length, ft.
= [0.785 x (1.0 ft.)2] x 1,640 ft.
= [0.785 x (1.0 ft. x 1.0 ft.)] x 1,640 ft.
= [0.785 x 1.0 ft2] x 1,640 ft.
= 0.785 ft2 x 1,640 ft.
3
Volume, ft = 1287.4 ft3
c. Convert Ft3 to gallons
Pipe capacity, gals = 1,287.4 ft3 x 7.48 gal/ft3
Pipe capacity, gals = 9630 gallons
5. X (Unknown) = Static pressure in pipeline
a. Convert psi to static head
Conversion factor: 1 psi = 2.31 ft.
# Ft. of Static Head = # psi x 2.31 ft./psi
= 75 psi x 2.31 ft./psi
# ft. of Static Head = 173.25
6. X (Unknown) = Velocity of fluid through pipe
a. Formula:
Velocity, ft./sec. = Q, ft.3/sec
Area, ft2
b. Convert Q, 200,000 gpd to Ft3/sec
MGD = 200,000 gal/day
1,000,000 gal/MG
MGD = 0.20 mgd
Conversion factor: 1.0 MGD = 1.55 ft3/sec
Ft3/sec = # MGD x 1.55 ft3/sec/mgd
Ft3/sec = 0.20 mgd x 1.55 ft3/sec/mgd
Ft3/sec = 0.31 ft3/sec
c. Calculate the area of the pipe, ft2
Convert 6 inches to feet:
!2
Ft. = 6 inches
12 inches/ft.
Ft. = 0.5 ft.
Area, ft2 = 0.785 x (D, ft2)
= 0.785 x (0.5 ft.)2
= 0.785 x (0.5 ft. x 0.5 ft.)
= 0.785 x 0.25 ft2
2
Area, ft = 0.20 ft2
d. Calculate the velocity of the fluid in the pipe:
Vel. ft.3/sec = 0.31 ft.3/sec
0.20 ft2
Vel. ft.3/sec = 1.55 ft./sec
7. X (Unknown) = Population loading, GPD/capital
a. Data:
Population = 27,000 persons
Pump Run Time = 10 hrs. in 24 hrs.
Pumping rate = 5,000 gpm
b. Formula:
GPD/cap. = Flow, gpd
# persons (capital)
c. Find number of gallons pumped in 24 hrs.
Convert 10 hrs. to mins./day of pumping run time:
Mins./day = 10 hrs./day x 60 mins./hr.
Mins./day = 600 mins./day
d. Calculate gallons per day of pumping
gal./day = 600 mins./day x 5,000 gals./day
gal./day = 3,000,000 gal./day
e. Calculate GPD of wastewater per person
GPD/cap = 3,000,000 gal./day
27,000 persons
GPD/cap = 111.11 gpd/capital
8. X (Unknown) = Lbs. of Chlorine dose needed per day
a. Data:
Flow = 1.0 mgd
Dose = 12 mg/L
!3
b. Formula:
Lbs. Chlorine/day Dose = Flow, mgd x Chemical concentration, mg/L x 8.34 lbs./gal
c. Calculate chlorine dosage:
Lbs. Chlorine/day Dose = 1.0 mgd x 12 mg/L x 8.34 lbs./gal
Lbs. Chlorine/day Dose = 100.1
9. V2 (Unknown) = Volume, gallons of 10% hypochlorite solution needed:
a. Formula:
V 1 x C1 = V 2 x C2
b. Data:
V1 = 250 gallons
V2 = New volume of 10% hypochlorite solution
C1 = 15% hypochlorite solution
C2 = 10% hypochlorite solution
c. Re-arrange formula to calculate V2:
V2 = V1 x C1
C2
V2 = 250 gals. x 15%
10%
V2 = 3750 gals.
10
V2 = 375 gallons
10. X (Unknown) = Volume of wastewater in pipe in gallons
a. Calculate volume of pipe in ft3 and then convert to gallons:
b. Convert 12-inch diameter to feet of diameter:
Ft. = 12 in.
12 in./ft.
Ft. = 1.0 ft.
c. Calculate the volume of the pipe in ft3:
Vol. ft3 = [0.785 x (D, ft.)2] x Length, ft.
Vol. ft3 = [0.785 x (1.0 ft.)2] x 100 ft.
Vol. ft3 = [0.785 x (1.0 ft. x 1.0 ft.)] x 100 ft.
Vol. ft3 = [0.785 x 1.0 ft.2] x 100 ft.
Vol. ft3 = 0.785 ft.2 x 100 ft.
Vol. ft3 = 78.5 ft3
d. Convert cubic foot volume to gallons:
!4
Capacity, gals = # ft3 x 7.48 gal/ft3
Capacity, gals = 78.5 ft3 x 7.48 gal/ft3
Capacity, gals = 587.2 gallons
11. X (Unknown) = # of psi at base of tower
a. Formula:
# psi = # of Feet
2.31 ft./psi
# psi = 230 ft.
2.31 ft./psi
# psi = 99.6 psi
12. X (Unknown) = concentration, mg/L of chemical
a. Formula:
mg/L = lbs./day of chemical
mgd x 8.34 lbs./gal
b. Convert 22 lbs./hr. of chemical to lbs. chemical/day
Lbs./day of chemical = 22 lbs./hr. x 24 hr./day
Lbs./day of chemical = 528 lbs./day
c. Convert 445 gpm to mgd:
Gal/day = 445 gal./min x 1440 mins./day
Gal/day = 640,800 gal/day
MGD = 640,800 gal/day
1,000,000 gals/MG
MGD = 0.641 mgd
d. Calculate concentration of chemical:
mg/L = 528 lbs./day
0.641 mgd x 8.34 lbs./gal
mg/L = 98.69 mg/L
13. X (Unknown) = Velocity of wastewater through the force main
a. Formula:
Velocity, ft./sec = Q, ft3/sec
Area, ft.2
!5
b. Convert 425 gpm to ft3/sec:
Ft3/min = 425 gal/min
7.48 gal/ft3
Ft3/min = 56.82 ft3/sec
Ft3/sec = 56.82 ft3/sec
60 sec/min
Ft3/sec = 0.95 ft3/sec
c. Calculate the area of the pipe:
Convert diameter of pipe from inches to feet:
Ft. = 8 inches
12 in/ft.
Ft. = 0.67 ft.
Area, ft2 = 0.785 x (D, ft.)2
= 0.785 x (0.67 ft.)2
= 0.785 x (0.67 ft. x 0.67 ft.)
= 0.785 x 0.45 ft2
2
Area, ft. = 0.35 ft.2
d. Calculate the velocity, ft./sec of wastewater through force main:
Velocity, ft./sec = 0.95 ft3/sec
0.35 ft2
Velocity, ft./sec = 2.7 ft./sec
14. X (Unknown) = Flow rate into the wet well in gpm
a. Data:
Length = 10 ft.
Width = 8 ft.
Velocity of the rise of water in well = 4 ft./6 mins. = 0.67 ft./min
b. Calculate the Q, flow rate in ft3/min and then convert to gpm flow rate
c. Formula for Q, flow rate;
Q, ft3/min = Area, ft2 x Velocity, ft./min
!6
d. Calculate area of wet well:
Area, ft2 = L, ft. x W, ft.
= 10 ft. x 8 ft.
Area, ft2 = 80 ft2
d. Calculate the flow in ft3/min then convert to gpm:
Q, ft3/min = 80 ft2 x 0.67 ft./min
Q, ft3/min = 53.6 ft3/min
Convert to gpm:
GPM = 53.6 ft3/min x 7.48 gal/ft3
GPM = 401 gpm
15. X (Unknown) = Labor cost for job task
a. Data:
Number of men on job = 2
Labor cost per hr./man = $14.00/hrs.
Total labor hrs. for each man = 10 hrs.
b. Calculate total labor hours for the job task:
2 operators x 10 hrs./operator = 20 hrs.
c. Calculate the labor cost for the job:
Total Labor Cost = 20 hrs. x $14.00/hr.
Total Labor Cost = $280.00
16. X (Unknown) = Volume of wastewater pipe will hold in gallons
a. Data:
Pipe length = 200 ft.
Pipe Diameter = 10 inches
1-inch of grease around diameter of pipe
Grease reduces the pipe diameter by 2 inches:
1-inch + 1-inch = 2 inches of FOG (1-inch of grease on both sides of diameter)
!7
New pipe diameter, inches = 10 inches – 2 inches
New pipe diameter, inches = 8 inches
b. Convert pipe diameter from inches to feet:
Ft. = 8 inches
12 in/ft.
Ft. = 0.67 ft.
c. Calculate volume of pipe in ft3:
Vol. ft3 = [0.785 x (D, ft.)2] x Length, ft.
= [0.785 x (0.67 ft.)2] x 200 ft.
= [0.785 x (0.67 ft. x 0.67 ft.)] x 200 ft.
= [0.785 x 0.45 ft.2] x 200 ft.
= 0.35 ft2 x 200 ft.
Vol. ft3 = 70 ft3
d. Convert 70 ft3 to gallons
Vol. gals = 70 ft3 x 7.48 gal/ft3
Vol. gals = 523.6 gallons or 524 gallons
17. X (Unknown) = % efficiency of the pump
18. X (Unknown) = brake horsepower capacity (bhp)
a. Data:
Flow = 8500 gpm
Total head, ft. = 39 ft.
Pump efficiency = 85% (.85 decimal form)
!8
b. Formula:
Brake Horsepower (bhp) = __(Flow, gpm) x (Head, ft.)________________
(3960) x (% Pump Effic. expressed as decimal)
c. Calculate the brake horsepower:
bhp = 8500 gpm x 39 ft.
3960 x .85
bhp = 331,500
3366
bhp = 98.48
19. X (Unknown) = Pumping rate, gpm for pump
a. Data:
Length = 8 ft.
Width = 7 ft.
Well drawdown, ft. = 3.5 ft.
Pump run time = 7 minutes
b. Formula:
gpm = Volume, gals in drawdown
Pump Run Time, mins
c. Calculate volume of water in drawdown in ft3 and then convert to gallons:
Vol. ft3 = L, ft. x W, ft. x Drawdown depth, ft.
= 8 ft. x 7 ft. x 3.5 ft.
= 196 ft3
Cap. gals = 196 ft3 x 7.48 gal/ft3
Cap. gals = 1466.1 gals
d. Calculate pumping rate (gpm)
gpm = 1466.1 gals
7 mins.
gpm = 209.4 gpm
20. X (Unknown) = Q, flow rate through pipe
a. Data:
Velocity = 2.0 ft./sec
Pipe Diameter = 18 inches
b. Formula:
Q, ft3/sec = Area, ft2 x Velocity, ft./sec
c. Calculate the area of the pipe:
!9
Convert 18-inch diameter to feet:
Ft. = 18 inches
12 in/ft.
Ft. = 1.5 ft.
Area, ft2 = 0.785 x (D, ft.)2
= 0.785 x (1.5 ft.)2
= 0.785 x (1.5 ft. x 1.5 ft.)
= 0.785 x 2.25 ft.2
2
Area, ft = 1.77 ft2
c. Calculate Q, flow rate through pipe:
Q, ft3/sec = Area, ft2 x Velocity, ft./sec
= 1.77 ft2 x 2.0 ft./sec
3
Q, ft /sec = 3.54 ft3/sec
21. X (Unknown) = Cost of electrical power to operate pump
a. Data:
Flow = 495 gpm
Total head, ft. = 300 ft.
Motor Efficiency = 70%
Electrical costs = $0.060 kWhr.
1.0 hp = 0.746 kilowatt
Pump Run Time = 12 hrs./day for 2 months (31 days in each month)
b. Calculate water horsepower (whp):
Whp = 495 gpm x 300 ft.
3960
Whp = 148,500
3960
Whp = 37.5
c. Find motor horsepower (mhp):
Mhp = ____whp________
Motor Effic. %
Mhp = 37.5 hp
.70
Mhp = 53.57
d. Calculate operating time for pump in hours:
!10
# Days pump operated in 2 months = 31 days/month + 31 days/month
# Days pump operated in 2 months = 62 days
Pump Operating Time, hrs. = 12 hrs./day x 62 days
Pump Operating Time, hrs. = 744 days
e. Calculate electrical cost:
Convert mhp to kilowatts:
Kilowatts = 53.57 mhp x 0.746 kW/hp
Kilowatts = 39.96
f. Calculate kilowatt hours:
kWhr = 39.96 kW x 744 hrs.
kWhr = 29,732.635
g. Calculate electrical cost:
Total Electrical Cost = 29,732.635 kWhr x $0.060/kWhr
Total Electrical Cost = $1783.96 or $1784.00
22. X (Unknown) = Yearly cost of chlorine
a. Data:
Flow = 70 gpm
Chlorine concentration = 11 mg/L
Chlorine costs = $0.77/lb.
1 year = 365 days
b. Find lbs./day of chlorine used:
Convert 70 gpm to mgd:
Gal/day = 70 gal/min x 1440 min/day
Gal/day = 100,800 gal/day
!11
mgd = 100,800 gal/day x 1,000,000 gal/MG
mgd = 0.101 mgd
Lbs. chlorine used/day = 0.101 mgd x 11 mg/L x 8.34 lbs./gal
Lbs. chlorine used/day = 9.26 or 9.3 lbs./day
c. Calculate cost of chlorine used per day:
Cl Cost, $/day = 9.3 lbs./day x $0.77/day
Cl Cost, $/day = $7.16/day
d. Calculate yearly chlorine cost:
Cost Cl/year = $7.16/day x 365 days/yr.
Cost Cl/year = $2614.00
23. One side of the grounds for a lift station is 325 ft. long. How many trees will be
required if the trees are to be 25 ft. apart with a tree at each end? Hint; draw a diagram of
the spacing of the trees.
*------*------*------*------*------*------*------*------*------*------*------*------*------*
1
2
3
4
5
6
7
8
9
10
11
12
13 14
* Represents a tree
Spaces between trees = 325 ft. = 13 spaces
25 ft.
14 trees are needed
!12