Statistics for Environmental Engineers

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10.7    Flow Dilution. The wastewater flow in a drain is estimated by adding to the upstream flow a 40,000 mg/L solution of compound A at a constant rate of 1 L/min and measuring the diluted A concentration downstream. The upstream (background) concentration of A is 25 mg/L. Five downstream measurements of A, taken within a short time period, are 200, 230, 192, 224, and 207. What is the best estimate of the wastewater flow, and what is the variance of this estimate?

10.8    Surface Area. The surface area of spherical particles is estimated from measurements on particle diameter. The formula is A = nD2. Derive a formula for the variance of the estimated surface areas. Prepare a diagram that shows how measurement error expands or contracts as a function of diameter.

10.9    Lab Procedure. For some experiment you have done, identify the possible sources of random and systematic error and explain how they would propagate into calculated values.


Laboratory Quality Assurance

KEY WORDS bias, control limit, corrective action, precision, quality assurance, quality control, range, Range chart, Shewhart chart, X (X-bar) chart, warning limit.

Engineering rests on making measurements as much as it rests on making calculations. Soil, concrete, steel, and bituminous materials are tested. River flows are measured and water quality is monitored. Data are collected for quality control during construction and throughout the operational life of the system. These measurements need to be accurate. The measured value should be close to the true (but unknown) value of the density, compressive strength, velocity, concentration, or other quantity being measured. Measurements should be consistent from one laboratory to another, and from one time period to another.

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