A circular copper tube with an inner diameter of 2 cm and a length of 100 m is used to transport drinking water. Water flows in the tube at an average velocity of 0.11 m/s at 20°C. At the inner tube surface, the mass concentration of copper in water is 50 g/m3. The Environmental Protection Agency (EPA) sets the standards for the National Primary Drinking Water Regulations (NPDWR) that apply to public water systems. The drinking water regulations limit the levels of contaminants in drinking water to protect public health. The maximum contaminant level for copper in drinking water, set by the NPDWR, is 1.3 mg/L. Above that, additional steps are required to treat the water before it is considered safe for the public. Determine whether the water from the tube has a safe level of copper as

Question

per the NPDWR. The diffusion coefficient for copper in water is 1.5 × 10?9 m2/s.

What will be an ideal response?

Answer 1

The inner surface of a tube for transporting water contains known concentration of copper. The level of copper in the water from the tube is to be determined.



Assumptions 1 The analogy between heat and mass transfer is applicable. 2 The flow is at steady state. 3 The flow is fully developed. 4 Mass concentration of copper on the tube surface is much greater than in the water flow, ?A, s>>?A, ?.



Properties The dynamic viscosity and density for water at 20°C are 1.002 × 10?3 kg/m?s and 998 kg/m3, respectively (Table A-9).



Analysis The Reynolds number of the flow is





So, the flow inside the tube is laminar. Based on the analogy between heat and mass transfer, the Nusselt and the Sherwood numbers in this case are Nu = Sh = 3.66. Hence,



The mass transfer coefficient becomes



The rate of mass convection of copper from the inner tube surface to the water is



At the tube inner surface, the mass concentration of copper in water is ?A, s = 50 g/m3; and for the water flow ?A, ?? 0,



The volumetric flow rate of water in the tube is



The level of copper in the water flowing from the tube is



Discussion Under the given conditions, the copper level in the water flowing out of the tube is almost twice the 1.3 mg/L limit set by the NPDWR. Therefore, the water is not safe for public use. Additional steps of treatment are necessary to reduce the copper contamination in the water.