D3 water distribution math worksheet
California D3 water distribution operator exam · 10 problems
Name: ______________________________ Date: ______________
Use the CA Exam Conversion Sheet (revised 4/30/2026) and a calculator.
1. A 0.9 MGD system doses dry alum at 31.5 mg/L. It costs $0.39 per lb. What is the chemical cost per day?
Chemical feed and solutions
- A) $236 per day
- B) $82.7 per day
- C) $11.1 per day
- D) $92.2 per day
2. A raw water reservoir holds 200 acre-feet. How many million gallons (MG) is that?
Unit conversions and pressure
- A) 72.7 MG
- B) 65.2 MG
- C) 487 MG
- D) 130 MG
3. A required CT is 50 mg·min/L and the free chlorine residual is 1.35 mg/L. What contact time is needed?
Chlorination and CT
- A) 67.5 min
- B) 55.5 min
- C) 37.0 min
- D) 48.7 min
4. A 10-inch main carries 785 GPM. What is the velocity in ft/sec?
Flow, velocity and detention
- A) 0.802 ft/sec
- B) 193 ft/sec
- C) 2.67 ft/sec
- D) 3.21 ft/sec
5. A trench for a new main is 280 ft long, 2 ft wide and 3 ft deep. How many cubic yards of soil must be removed?
Area and volume
- A) 187 yd³
- B) 465 yd³
- C) 62.2 yd³
- D) 560 yd³
6. A well's pumping water level is 382 ft below ground and its drawdown is 91 ft. What was the static water level before pumping?
Wells, pumps and power
- A) 91.0 ft
- B) 291 ft
- C) 382 ft
- D) 473 ft
7. An 8.9 MGD system doses dry hydrated lime at 10.5 mg/L. It costs $0.18 per lb. What is the chemical cost per day?
Chemical feed and solutions
- A) $16.8 per day
- B) $126 per day
- C) $779 per day
- D) $140 per day
8. A flow transmitter is scaled 4 mA = 0 GPM and 20 mA = 2,400 GPM. The SCADA input reads 10.7 mA. What flow does that represent?
Unit conversions and pressure
- A) 804 GPM
- B) 1,610 GPM
- C) 1,010 GPM
- D) 1,280 GPM
9. A 620,000-gallon storage tank is to be disinfected at 25 mg/L using 65% HTH (calcium hypochlorite). How many pounds of HTH are needed?
Chlorination and CT
- A) 199 lbs
- B) 398 lbs
- C) 249 lbs
- D) 299 lbs
10. Water flows through an 18-inch main at 4.1 ft/sec. What is the flow in GPM?
Flow, velocity and detention
- A) 2,170 GPM
- B) 1,630 GPM
- C) 3,250 GPM
- D) 54.2 GPM
Answer key: D3 water distribution math worksheet
1. D) $92.2 per day
1. lbs/day = MGD × mg/L × 8.34 (the sheet's "ppm or mg/L" line solved for lbs) [Sheet p.2, Chemical Dosage Calculations: "ppm or mg/L = lbs / (MG x 8.34)"] = 0.9 × 31.5 × 8.34 = 236.439 lbs/day. 2. Cost/Day = Lbs/Day × Cost/lb [Sheet p.1, Other: "Cost/Day ($) = Lbs/Day x Cost/lb ($)"] = 236.439 × $0.39 = $92.21 per day. 3. Answer: $92.2 per day (rounded to 3 significant figures).
Source: CA Exam Conversion Sheet (Revised 4/30/2026), p.2, Chemical Dosage Calculations: "ppm or mg/L = lbs / (MG x 8.34)"; p.1, Other: "Cost/Day ($) = Lbs/Day x Cost/lb ($)"
2. B) 65.2 MG
1. 1 AF = 325,851 Gal [Sheet p.1, Units and Conversion Factors, row 4: "1 AF = 325,851 Gal"]. 2. Gallons = 200 AF × 325,851 = 65,170,200 gal. 3. MG = gallons ÷ 1,000,000 [Sheet p.1, Unit Definition: "MG Million Gallons" (1 MG = 1,000,000 gal)] = 65.1702 MG. 4. Answer: 65.2 MG (rounded to 3 significant figures).
Source: CA Exam Conversion Sheet (Revised 4/30/2026), p.1, Units and Conversion Factors, row 4: "1 AF = 325,851 Gal"; p.1, Unit Definition: "MG Million Gallons" (1 MG = 1,000,000 gal)
3. C) 37.0 min
1. Time (min) = C × T ÷ Chlorine Residual [Sheet p.2, C x T Calculations: "Time (min) = C x T / Chlorine Residual (mg/L)"] = 50 ÷ 1.35 = 37.04 min. 2. Answer: 37.0 min (rounded to 3 significant figures).
Source: CA Exam Conversion Sheet (Revised 4/30/2026), p.2, C x T Calculations: "Time (min) = C x T / Chlorine Residual (mg/L)"
4. D) 3.21 ft/sec
1. Q = 785 GPM ÷ 448.8 GPM/CFS = 1.749 ft³/sec [Sheet p.1, Units and Conversion Factors, row 7: "1 CFS = 448.8 GPM"]. 2. A = .785 × (10 ÷ 12)² = 0.5451 ft² [Sheet p.1, Area and Volume: "Area of Circle = .785 X D2"]. 3. V = Q ÷ A [Sheet p.1, Flow & Velocity: "V (Ft/Sec) = Q (Ft3/Sec) / A (Ft2)"] = 1.749 ÷ 0.5451 = 3.209 ft/sec. 4. Answer: 3.21 ft/sec (rounded to 3 significant figures).
Source: CA Exam Conversion Sheet (Revised 4/30/2026), p.1, Units and Conversion Factors, row 7: "1 CFS = 448.8 GPM"; p.1, Area and Volume: "Area of Circle = .785 X D2"; p.1, Flow & Velocity: "V (Ft/Sec) = Q (Ft3/Sec) / A (Ft2)"
5. C) 62.2 yd³
1. Volume = L × W × D = 280 × 2 × 3 = 1,680 ft³. 2. 1 yd³ = 27 Ft³ [Sheet p.1, Units and Conversion Factors, row 34: "1 yd3 = 27 Ft3"]: 1,680 ÷ 27 = 62.22 yd³. 3. Answer: 62.2 yd³ (rounded to 3 significant figures).
Source: CA Exam Conversion Sheet (Revised 4/30/2026), p.1, Units and Conversion Factors, row 34: "1 yd3 = 27 Ft3"
6. B) 291 ft
1. Drawdown = pumping water level − static water level (the denominator of [Sheet p.1, Pumping: "Specific Capacity (GPM/Ft) = Well Yield (GPM) / Drawdown (Ft)"]), so static water level = pumping water level − drawdown. 2. = 382 − 91 = 291 ft below ground. 3. Answer: 291 ft.
Source: CA Exam Conversion Sheet (Revised 4/30/2026), p.1, Pumping: "Specific Capacity (GPM/Ft) = Well Yield (GPM) / Drawdown (Ft)"
7. D) $140 per day
1. lbs/day = MGD × mg/L × 8.34 (the sheet's "ppm or mg/L" line solved for lbs) [Sheet p.2, Chemical Dosage Calculations: "ppm or mg/L = lbs / (MG x 8.34)"] = 8.9 × 10.5 × 8.34 = 779.373 lbs/day. 2. Cost/Day = Lbs/Day × Cost/lb [Sheet p.1, Other: "Cost/Day ($) = Lbs/Day x Cost/lb ($)"] = 779.373 × $0.18 = $140.3 per day. 3. Answer: $140 per day (rounded to 3 significant figures).
Source: CA Exam Conversion Sheet (Revised 4/30/2026), p.2, Chemical Dosage Calculations: "ppm or mg/L = lbs / (MG x 8.34)"; p.1, Other: "Cost/Day ($) = Lbs/Day x Cost/lb ($)"
8. C) 1,010 GPM
1. Process Units = (Live Signal − 4 mA) × Process Range ÷ 16 mA [Sheet p.1, Electrical/SCADA: "Process Units = (Live Signal (mA) - 4 mA) x Process Range / 16 mA"]. 2. (10.7 − 4) = 6.7 mA; 6.7 × 2,400 ÷ 16 = 1,005 GPM. 3. Answer: 1,010 GPM (rounded to 3 significant figures).
Source: CA Exam Conversion Sheet (Revised 4/30/2026), p.1, Electrical/SCADA: "Process Units = (Live Signal (mA) - 4 mA) x Process Range / 16 mA"
9. A) 199 lbs
1. MG = 620,000 ÷ 1,000,000 = 0.62 MG [Sheet p.1, Unit Definition: "MG Million Gallons" (1 MG = 1,000,000 gal)]. 2. HTH Solid (lbs) = MG × mg/L × 8.34 ÷ (Strength/100) [Sheet p.1, Chlorination: "HTH Solid (lbs) = MG x mg/L x 8.34 / (Strength (%)/100)"]. 3. = 0.62 × 25 × 8.34 ÷ 0.65 = 129.27 ÷ 0.65 = 198.9 lbs. 4. Answer: 199 lbs (rounded to 3 significant figures).
Source: CA Exam Conversion Sheet (Revised 4/30/2026), p.1, Unit Definition: "MG Million Gallons" (1 MG = 1,000,000 gal); p.1, Chlorination: "HTH Solid (lbs) = MG x mg/L x 8.34 / (Strength (%)/100)"
10. C) 3,250 GPM
1. A = .785 × D² [Sheet p.1, Area and Volume: "Area of Circle = .785 X D2"] = .785 × (18 ÷ 12)² = 1.76625 ft² [12 in = 1 ft]. 2. Q = A × V [Sheet p.1, Flow & Velocity: "(Q) Flow (Ft3/Sec) = (A) Area (Ft2) x (V) Velocity (Ft/Sec)"] = 1.76625 × 4.1 = 7.242 ft³/sec. 3. 1 CFS = 448.8 GPM [Sheet p.1, Units and Conversion Factors, row 7: "1 CFS = 448.8 GPM"]: 7.242 × 448.8 = 3,250 GPM. 4. Answer: 3,250 GPM (rounded to 3 significant figures). 5. If you used 1.55 CFS per MGD (Units row 28) and 694.4 GPM per MGD (row 29) instead of 448.8 GPM per CFS (row 7), you get 3,240 GPM. The sheet prints both factors, so either answer is right; pick the option closest to yours.
Source: CA Exam Conversion Sheet (Revised 4/30/2026), p.1, Area and Volume: "Area of Circle = .785 X D2"; p.1, Flow & Velocity: "(Q) Flow (Ft3/Sec) = (A) Area (Ft2) x (V) Velocity (Ft/Sec)"; p.1, Units and Conversion Factors, row 7: "1 CFS = 448.8 GPM"