The article “Effect of Varying Solids Concentration and Organic Loading on the Performance of Temperature Phased Anaerobic Digestion Process” (S. Vandenburgh and T. Ellis, Water Environment Research, 2002:142-148) discusses experiments to determine the effect of the solids concentration on the performance of treatment methods for wastewater sludge. In the first experiment, the concentration of solids (in g/L) was 43.94 ± 1.18. In the second experiment, which was independent of the first, the concentration was 48.66 ± 1.76. Estimate the difference in the concentration between the two experiments, and find the uncertainty in the estimate.
Step1 of 3:
Let us consider X be the concentration of solid in the first Experiment and Y be the concentration of solid in the second Experiment.
X = 43.94, and Y = 48.66,
We need to estimate the difference in the concentration between the two experiments, and find the uncertainty in the estimate.
Step2 of 3:
The difference in the concentration between the two experiments is given by
Hence, T = 4.72.
1).Differentiate with respect X then we get
Let u = X - Y
du = 1
Apply chain rule then we get
Substitute “u” value in above equation we get
Hence, = -1.
Step3 of 3:
2).Differentiate with respect Y then we get