What is the diameter of the pipe in the 50.1 mg/L dosage problem?

• A. 24.0 in
• B. 20.0 in
• C. 18.0 in
• D. 26.0 in

Answer: (A)

Sizing the pipe for a 50.1 mg/L dosage hinges on how much water is moving through the pipe and how that flow relates to the pipe’s cross‑sectional area. The chemical dose is tied to the water flow: the amount of chemical delivered each second equals the desired concentration times the flow rate. To size the pipe, use the flow equation Q = A V, where A is the cross‑sectional area of the pipe (A = πD^2/4) and V is the flow velocity. Rearranging gives D = sqrt(4Q/(πV)).

If the problem provides a specific flow rate and a target velocity (or allows a standard design velocity), plug those values in to solve for D. In this case, those numbers yield a diameter of 24 inches. The other diameter options would not provide the same area required to carry the given flow at the specified velocity, so they wouldn’t achieve the desired dosage at the pipe’s output.