Question

# Problem S-28. Background. Lead contamination of water in older buildings often comes from lead pipes used to carry drinking water. Although the water chemistry can get complicated, over time a

solid lead carbonate (PbCO3) corrosion layer can build up and line the inner surface these pipes. At a drinking water pH of 8 and above, the lead carbonate corrosion layer is not very soluble in water. However, if the water pH is lowed to pH 7 or below, and if dissolved chlorine (Cl2) is also present in the water, then lead carbonate reacts to form lead chloride (PbCl2), which is soluble in water. This process renders lead of limited solubility at the interface of the corrosion layer and the water flowing through the pipe. For example, at pH 7 and 20 oC, the solubility of lead is 0.630 mmol/m3 (CAL*) and the diffusion coefficient of PbCl2 dissolved in water is 1.95 x 10-5 cm2/sec. The lead concentration of drinking water that is considered safe by the U.S. EPA is 15 µg/L (0.072 mmol/m3). 1000 mmol = 1 gmol. Additional properties for water: u = 0.010 g/cm-sec, p = 1.0 g/cm3. properties for water: u = 0.010 g/cm-sec, p= 1.0 g/cm3.Problem Statement. Drinking water at pH 7 flows through a corroded lead pipe of 2.0 cm inner diameterand 16 m length at volumetric flowrate of 62.8 cm3/sec (1.0 gal/min) (Figure 1). A 12 m section of theinner surface of the pipe is uniformly corroded with lead carbonate at the region shown in Figure 1. Estimate the mass transfer coefficient (kL) of lead chloride (solute A) in water flowing through thepipe.а. b. What is the soluble lead concentration in the drinking water exiting the pipe, CAL? As part of your analysis, perform a material balance for solute A on a differential volume element of the pipe, and then integrate to get the final model. Is this water safe to drink? с.Often, a low flow of water can make the concentration of dissolved lead in the pipe flow even higher.Assume that “fully-developed laminar flow" exists inside the pipe. What is the new kL under this condition? If the bulk fluid velocity vo is increased, with all other parameters kept constant, kL (1) is not affected; (2) increases by væ0.2; (3) increases by v20.83 If the fluid velocity is vo is increased, with all other parameters kept constant, CAL (1) is not affected; (2) increases; (3) decreases

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