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Unformatted text preview: 1 CEE 350 Winter 2012 Homework #2 Solution Problem 1 (Textbook Problem 1.14, 0.6 points) Ozone is sometimes used as a disinfectant in drinking water. Ozone is highly reactive. It will react with many benign species as well as pathogens it is intended to kill. It is found that ozone reaction in a particular water source follows a first-order kinetic pattern. Specifically, measurements have shown that in this water the ozone concentration decreases by 50% in 12 minutes (t 1/2 =12 min). To treat this water, engineers want to inject ozone into a pipe bringing this water to a treatment plant. That pipe has a 3-ft diameter, is 3,400 feet long with a steady flow of 10,000 gal/min. What concentration of ozone should be present at the head of the pipe so that there will be an ozone concentration of 1.0 mg/L at the pipe’s exit into the plant? What should be the concentration at the injection point if the flow decreases to 5,000 gal/min? The pipe is assumed to act as an ideal PFR. First, we need to determine the apparent first order rate of ozone in this water: ¡ ¢ 1 2 / 1 min 0575 . 12 69 . 69 . £ t k Second, we will treat the system as a PFR. Therefore, the expression for the concentration of ozone at the injection point is ¸ ¹ · ¨ © § £ l U k C C exp where U is the linear velocity of the movement of water in the pipe, and l is its length. Given the condition of the problem, we can define U as follows 2 4 d Q A Q U c S For the sake of consistence, we will use linear units henceforth. The indicate that the diameter of the pipe and its length is 0.914 m and 1036.3 m, respectively, while the flow rates are 37.9 and 18.95 m 3 /min, respectively. The linear velocity of water in the pipe at these flow rates are then 57.7 and 28.9 m/min, respectively. Using these data, we can determine the required initial concentration of ozone using this expression ¸ ¹ · ¨ © § l U k C C exp 2 Calculations using this formula yield the initial concentration of ozone of 2.8 and 7.9 mg/L for flows 10,000 and 5,000 gal/min, respectively. The data are also shown in the table below....
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This note was uploaded on 03/31/2012 for the course CEE 350 taught by Professor Korshin during the Spring '10 term at University of Washington.
- Spring '10