WATER MATH MASTERY 200
PRACTICE PROBLEMS WITH
STEP BY STEP RATIONALES
DISTRIBUTION OPERATOR
CERTIFICATION EXAM PREP
Water Distribution Math Practice Exam
1. A water tank is 20 feet high and currently full. What is the pressure
in psi at the bottom of the tank?
A. 46.2 psi
B. 8.66 psi
C. 43.3 psi
D. 9.24 psi
Rationale: Pressure (psi) = Head (ft) / 2.31. Calculation: .31
= 8.66 psi.
2. How many gallons of water are contained in a pipe that is 10 inches
in diameter and 500 feet long?
A. 1,540 gallons
B. 2,310 gallons
C. 2,040 gallons
D. 2,720 gallons
Rationale: Volume = 0.785 × D² × L × 7.48. Calculation: 0.785 ×
(0.833 ft)² × 500 ft × 7.48 = 2,040 gallons.
3. A chlorinator is set to deliver 15 lbs of chlorine in 24 hours to a
flow of 1.2 MGD. What is the chlorine dosage in mg/L?
A. 1.2 mg/L
B. 1.5 mg/L
C. 1.8 mg/L
D. 2.1 mg/L
Rationale: Dosage (mg/L) = lbs / (Flow MGD × 8.34).
Calculation: 15 / (1.2 × 8.34) = 1.5 mg/L.
,4. Convert a flow of 450 gallons per minute (gpm) to cubic feet per
second (cfs).
A. 0.50 cfs
B. 1.00 cfs
C. 1.50 cfs
D. 2.00 cfs
Rationale: 1 cfs = 448.8 gpm. Calculation: .8 = 1.00 cfs.
5. A rectangular basin is 40 feet long, 20 feet wide, and 10 feet deep.
What is the volume in gallons?
A. 6,000 gallons
B. 45,670 gallons
C. 59,840 gallons
D. 80,000 gallons
Rationale: Volume = L × W × D × 7.48. Calculation: 40 × 20 × 10
× 7.48 = 59,840 gallons.
6. What is the "Water Horsepower" (WHP) required to pump 300
gpm against a total head of 150 feet?
A. 9.2 WHP
B. 11.4 WHP
C. 13.8 WHP
D. 15.1 WHP
Rationale: WHP = (gpm × Head) / 3,960. Calculation: (300 ×
150) / 3,960 = 11.36 WHP.
7. If a pressure gauge at the bottom of a hill reads 65 psi, how many
feet of head are acting on the gauge?
A. 28.1 ft
B. 135 ft
C. 150 ft
D. 165 ft
Rationale: Head (ft) = psi × 2.31. Calculation: 65 × 2.31 = 150.15
ft.
8. How many pounds of 65% calcium hypochlorite are needed to dose
a 250,000-gallon tank at 20 mg/L?
A. 41.7 lbs
B. 64.2 lbs
C. 32.1 lbs
D. 55.5 lbs
, Rationale: lbs = (MG × mg/L × 8.34) / % Purity. Calculation:
(0.25 × 20 × 8.34) / 0.65 = 64.15 lbs.
9. A pump runs for 8 hours and delivers 240,000 gallons. What is the
pumping rate in gpm?
A. 300 gpm
B. 500 gpm
C. 750 gpm
D. 1,000 gpm
Rationale: gpm = Total Gallons / Minutes. Calculation: 240,000 /
(8 × 60) = 500 gpm.
10. What is the circumference of a circular storage tank with a
diameter of 50 feet?
A. 78.5 ft
B. 157.1 ft
C. 1,962 ft
D. 314 ft
Rationale: Circumference = π × D. Calculation: 3.14159 × 50 =
157.08 ft.
11. A 12-inch pipe is 1,000 feet long. If the velocity of the water is 3
feet per second, what is the flow in gpm?
A. 880 gpm
B. 1,058 gpm
C. 1,225 gpm
D. 1,500 gpm
Rationale: Flow (cfs) = Area × Velocity. Area = 0.785 × 1². Flow =
0.785 × 3 = 2.355 cfs. cfs to gpm: 2.355 × 448.8 = 1,057 gpm.
12.A tank has a radius of 15 feet and is 25 feet high. What is the total
volume in cubic feet?
A. 1,177 cu ft
B. 5,300 cu ft
C. 17,663 cu ft
D. 22,100 cu ft
Rationale: Volume = π × r² × h. Calculation: 3.14159 × 15² × 25 =
17,663 cu ft.
13.To achieve a chlorine residual of 0.5 mg/L with a chlorine demand
of 1.8 mg/L, what should the dosage be?
A. 1.3 mg/L
B. 2.3 mg/L
, C. 0.9 mg/L
D. 3.0 mg/L
Rationale: Dosage = Demand + Residual. Calculation: 1.8 + 0.5 =
2.3 mg/L.
14.How many pounds of chlorine gas are required to treat 2,500,000
gallons of water at a dosage of 2.0 mg/L?
A. 20.8 lbs
B. 41.7 lbs
C. 50.0 lbs
D. 83.4 lbs
Rationale: lbs = MG × mg/L × 8.34. Calculation: 2.5 × 2.0 × 8.34
= 41.7 lbs.
15. What is the area of a circle with a diameter of 24 inches in square
feet?
A. 4.52 sq ft
B. 3.14 sq ft
C. 6.28 sq ft
D. 12.56 sq ft
Rationale: Area = 0.785 × D². 24 inches = 2 ft. Calculation: 0.785
× 2² = 3.14 sq ft.
16.A flow of 2.5 MGD is equivalent to how many gallons per minute?
A. 1,250 gpm
B. 1,736 gpm
C. 2,100 gpm
D. 3,600 gpm
Rationale: gpm = (MGD × 1,000,000) / 1,440. Calculation:
2,500,,440 = 1,736.1 gpm.
17. If a chemical scale shows a decrease of 32 lbs over a 24-hour period
while treating 1.5 MGD, what was the dosage?
A. 2.1 mg/L
B. 2.56 mg/L
C. 3.2 mg/L
D. 1.8 mg/L
Rationale: mg/L = lbs / (MGD × 8.34). Calculation: 32 / (1.5 ×
8.34) = 2.56 mg/L.
18. A water line has a pressure of 85 psi. What is the equivalent
head in feet?
A. 36.8 ft
PRACTICE PROBLEMS WITH
STEP BY STEP RATIONALES
DISTRIBUTION OPERATOR
CERTIFICATION EXAM PREP
Water Distribution Math Practice Exam
1. A water tank is 20 feet high and currently full. What is the pressure
in psi at the bottom of the tank?
A. 46.2 psi
B. 8.66 psi
C. 43.3 psi
D. 9.24 psi
Rationale: Pressure (psi) = Head (ft) / 2.31. Calculation: .31
= 8.66 psi.
2. How many gallons of water are contained in a pipe that is 10 inches
in diameter and 500 feet long?
A. 1,540 gallons
B. 2,310 gallons
C. 2,040 gallons
D. 2,720 gallons
Rationale: Volume = 0.785 × D² × L × 7.48. Calculation: 0.785 ×
(0.833 ft)² × 500 ft × 7.48 = 2,040 gallons.
3. A chlorinator is set to deliver 15 lbs of chlorine in 24 hours to a
flow of 1.2 MGD. What is the chlorine dosage in mg/L?
A. 1.2 mg/L
B. 1.5 mg/L
C. 1.8 mg/L
D. 2.1 mg/L
Rationale: Dosage (mg/L) = lbs / (Flow MGD × 8.34).
Calculation: 15 / (1.2 × 8.34) = 1.5 mg/L.
,4. Convert a flow of 450 gallons per minute (gpm) to cubic feet per
second (cfs).
A. 0.50 cfs
B. 1.00 cfs
C. 1.50 cfs
D. 2.00 cfs
Rationale: 1 cfs = 448.8 gpm. Calculation: .8 = 1.00 cfs.
5. A rectangular basin is 40 feet long, 20 feet wide, and 10 feet deep.
What is the volume in gallons?
A. 6,000 gallons
B. 45,670 gallons
C. 59,840 gallons
D. 80,000 gallons
Rationale: Volume = L × W × D × 7.48. Calculation: 40 × 20 × 10
× 7.48 = 59,840 gallons.
6. What is the "Water Horsepower" (WHP) required to pump 300
gpm against a total head of 150 feet?
A. 9.2 WHP
B. 11.4 WHP
C. 13.8 WHP
D. 15.1 WHP
Rationale: WHP = (gpm × Head) / 3,960. Calculation: (300 ×
150) / 3,960 = 11.36 WHP.
7. If a pressure gauge at the bottom of a hill reads 65 psi, how many
feet of head are acting on the gauge?
A. 28.1 ft
B. 135 ft
C. 150 ft
D. 165 ft
Rationale: Head (ft) = psi × 2.31. Calculation: 65 × 2.31 = 150.15
ft.
8. How many pounds of 65% calcium hypochlorite are needed to dose
a 250,000-gallon tank at 20 mg/L?
A. 41.7 lbs
B. 64.2 lbs
C. 32.1 lbs
D. 55.5 lbs
, Rationale: lbs = (MG × mg/L × 8.34) / % Purity. Calculation:
(0.25 × 20 × 8.34) / 0.65 = 64.15 lbs.
9. A pump runs for 8 hours and delivers 240,000 gallons. What is the
pumping rate in gpm?
A. 300 gpm
B. 500 gpm
C. 750 gpm
D. 1,000 gpm
Rationale: gpm = Total Gallons / Minutes. Calculation: 240,000 /
(8 × 60) = 500 gpm.
10. What is the circumference of a circular storage tank with a
diameter of 50 feet?
A. 78.5 ft
B. 157.1 ft
C. 1,962 ft
D. 314 ft
Rationale: Circumference = π × D. Calculation: 3.14159 × 50 =
157.08 ft.
11. A 12-inch pipe is 1,000 feet long. If the velocity of the water is 3
feet per second, what is the flow in gpm?
A. 880 gpm
B. 1,058 gpm
C. 1,225 gpm
D. 1,500 gpm
Rationale: Flow (cfs) = Area × Velocity. Area = 0.785 × 1². Flow =
0.785 × 3 = 2.355 cfs. cfs to gpm: 2.355 × 448.8 = 1,057 gpm.
12.A tank has a radius of 15 feet and is 25 feet high. What is the total
volume in cubic feet?
A. 1,177 cu ft
B. 5,300 cu ft
C. 17,663 cu ft
D. 22,100 cu ft
Rationale: Volume = π × r² × h. Calculation: 3.14159 × 15² × 25 =
17,663 cu ft.
13.To achieve a chlorine residual of 0.5 mg/L with a chlorine demand
of 1.8 mg/L, what should the dosage be?
A. 1.3 mg/L
B. 2.3 mg/L
, C. 0.9 mg/L
D. 3.0 mg/L
Rationale: Dosage = Demand + Residual. Calculation: 1.8 + 0.5 =
2.3 mg/L.
14.How many pounds of chlorine gas are required to treat 2,500,000
gallons of water at a dosage of 2.0 mg/L?
A. 20.8 lbs
B. 41.7 lbs
C. 50.0 lbs
D. 83.4 lbs
Rationale: lbs = MG × mg/L × 8.34. Calculation: 2.5 × 2.0 × 8.34
= 41.7 lbs.
15. What is the area of a circle with a diameter of 24 inches in square
feet?
A. 4.52 sq ft
B. 3.14 sq ft
C. 6.28 sq ft
D. 12.56 sq ft
Rationale: Area = 0.785 × D². 24 inches = 2 ft. Calculation: 0.785
× 2² = 3.14 sq ft.
16.A flow of 2.5 MGD is equivalent to how many gallons per minute?
A. 1,250 gpm
B. 1,736 gpm
C. 2,100 gpm
D. 3,600 gpm
Rationale: gpm = (MGD × 1,000,000) / 1,440. Calculation:
2,500,,440 = 1,736.1 gpm.
17. If a chemical scale shows a decrease of 32 lbs over a 24-hour period
while treating 1.5 MGD, what was the dosage?
A. 2.1 mg/L
B. 2.56 mg/L
C. 3.2 mg/L
D. 1.8 mg/L
Rationale: mg/L = lbs / (MGD × 8.34). Calculation: 32 / (1.5 ×
8.34) = 2.56 mg/L.
18. A water line has a pressure of 85 psi. What is the equivalent
head in feet?
A. 36.8 ft
