A pipe 2.5 ft in diameter, 4,408 ft long, is disinfected with 12.5% sodium hypochlorite solution. If the desired dose is 25 mg/L, how many gallons of sodium hypochlorite are needed?

• A. 18.8 gal
• B. 23 gal
• C. 26 gal
• D. 29.6 gal

Answer: (C)

The test is about figuring how much disinfectant solution is needed to deliver a specific amount of chlorine to the water in a pipe.

First determine the water volume in the pipe. The pipe has a diameter of 2.5 ft, so the radius is 1.25 ft. The cross-sectional area is πr^2 = π(1.25)^2 ≈ 4.909 ft^2. Multiply by the length (4,408 ft) to get a water volume of about 21,649 ft^3. Convert to liters: 21,649 ft^3 × 28.3168 ≈ 613,000 L of water.

With a desired dose of 25 mg/L, the total NaOCl mass needed is 613,000 L × 25 mg/L ≈ 15,325,000 mg ≈ 15.3 kg of NaOCl.

Now translate that into gallons of 12.5% sodium hypochlorite solution. A typical density for this solution is about 1.25 kg/L. Each liter of solution contains NaOCl mass of 12.5% of 1.25 kg = 0.15625 kg (156 g) of NaOCl. Per gallon (3.785 L), that’s about 156 g/L × 3.785 ≈ 590 g of NaOCl per gallon.

Required gallons ≈ 15,315 g NaOCl / 590 g per gallon ≈ 25.9 gallons, i.e., about 26 gallons.