Statistics for Environmental Engineers

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Propagation of Error in Measured Particle Diameter into Error in the Computed Particle Diameter


TABLE 10.2


D


0.5


0.75


0.798


1


1.25


1.5


V


0.065


0.221


0.266


0.524


1.023


1.767


d


0.00006


0.00031


0.00040


0.00099


0.00241


0.00500


d


0.008


0.018


0.020


0.031


0.049


0.071


dV/dD


0.393


0.884


1.000


1.571


2.454


3.534


dV/ dD


0.154


0.781


1.000


2.467


6.024


12.491

Preliminary investigations of error transmission can be a valuable part of experimental planning. If, as was assumed here, the magnitude of the measurement error is the same for all diameters, a greater number of particles should be measured and used to estimate V if the particles are large.

Case Study: Calcium Carbonate Scaling in Water Mains


A small layer of calcium carbonate scale on water mains protects them from corrosion, but heavy scale reduces the hydraulic capacity. Finding the middle ground (protection without damage to pipes) is a matter of controlling the pH of the water. Two measures of the tendency to scale or corrode are the Langlier saturation index (LSI) and the Ryznar stability index (RSI). These are:


LSI = pH — pHs RSI = 2pHs — pH


where pH is the measured value and pHs the saturation value. pH is a calculated value that is a function of temperature (T), total dissolved solids concentration (TDS), alkalinity [Alk], and calcium concentration [Ca]. [Alk] and [Ca] are expressed as mg/L equivalent CaCO3. The saturation pH is pHs = A — log10[Ca] — log10[Alk], where A = 9.3 + log10(K/K2) + ■2+-y-=, in which ^ is the ionic strength. Ks, a solubility product, and K2, an ionization constant, depend on temperature and TDS.

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