Question

A treatment plant has been designed with the capability to add hydrofluosilicic acid. The mixer installed at the point of chemical addition is warranted to achieve a COV of 5 percent across the cross section of flow at the point where the automatic analyzer draws samples for analysis. In a performance test during plant startup (commissioning) samples were taken at nine representative points across the cross section and the results are reported below. Determine if the mixer is meeting its specification Fluoride, mg/L Sample Point 1.02 1 2 3 1.20 0.95 0.90 4 5 1.10 0.85 0.95 0.98 6 7 9 0.95

Answer 1

Mean ($\mu$) = (1.02 + 1.2 + 0.95 + 0.9 + 1.1 + 0.85 + 0.95 + 0.98 + 0.95) / 9 = 0.989 mg/L

Standard Deviation ($\sigma$) = (((1.02-0.989)²+(1.2-0.989)²+(0.95-0.989)²+(0.9-0.989)²+(1.1-0.989)²+(0.85-0.989)²+(0.95-0.989)²+(0.98-0.989)²+(0.95-0.989)²) / (9-1))^0.5 = 0.106 mg/L

Coefficient of Variation (COV) = $\sigma$ / $\mu$ = 0.106 / 0.989 = 0.107 or 10.7 %

Since COV > 5 %, the mixer is not meeting its specification.