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Flow, velocity and detention: California D1 water distribution operator math

Q = A x V, fill rates, detention time, surface loading.

Below are 3 worked examples. Each answer is computed with the formulas and constants on the CA Exam Conversion Sheet (revised 4/30/2026), and the solution names the line it uses.

Formulas from the sheet for this topic

Example 1. Water flows through a 36-inch main at 4.9 ft/sec. What is the flow in GPM?

  1. A) 259 GPM
  2. B) 62,100 GPM
  3. C) 15,500 GPM
  4. D) 5,180 GPM
Show the answer and worked solution

Answer: C) 15,500 GPM

1. A = .785 × D² [Sheet p.1, Area and Volume: "Area of Circle = .785 X D2"] = .785 × (36 ÷ 12)² = 7.065 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)"] = 7.065 × 4.9 = 34.6185 ft³/sec. 3. 1 CFS = 448.8 GPM [Sheet p.1, Units and Conversion Factors, row 7: "1 CFS = 448.8 GPM"]: 34.6185 × 448.8 = 15,537 GPM. 4. Answer: 15,500 GPM (rounded to 3 significant figures).

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"

Example 2. Water flows through a 20-inch main at 2.3 ft/sec. What is the flow in GPM?

  1. A) 4,500 GPM
  2. B) 9,000 GPM
  3. C) 3,480 GPM
  4. D) 2,250 GPM
Show the answer and worked solution

Answer: D) 2,250 GPM

1. A = .785 × D² [Sheet p.1, Area and Volume: "Area of Circle = .785 X D2"] = .785 × (20 ÷ 12)² = 2.181 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)"] = 2.181 × 2.3 = 5.0163 ft³/sec. 3. 1 CFS = 448.8 GPM [Sheet p.1, Units and Conversion Factors, row 7: "1 CFS = 448.8 GPM"]: 5.0163 × 448.8 = 2,251 GPM. 4. Answer: 2,250 GPM (rounded to 3 significant figures).

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"

Example 3. Water flows through a 16-inch main at 3.6 ft/sec. What is the flow in GPM?

  1. A) 1,130 GPM
  2. B) 37.6 GPM
  3. C) 2,250 GPM
  4. D) 1,690 GPM
Show the answer and worked solution

Answer: C) 2,250 GPM

1. A = .785 × D² [Sheet p.1, Area and Volume: "Area of Circle = .785 X D2"] = .785 × (16 ÷ 12)² = 1.3956 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)"] = 1.3956 × 3.6 = 5.02416 ft³/sec. 3. 1 CFS = 448.8 GPM [Sheet p.1, Units and Conversion Factors, row 7: "1 CFS = 448.8 GPM"]: 5.02416 × 448.8 = 2,254.8 GPM. 4. Answer: 2,250 GPM (rounded to 3 significant figures).

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"

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