DIFFUSION_SOLUTION - ENV 6015 Solutions to Diffusion...

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1 ENV 6015 Solutions to Diffusion Problem Set 1. Salt water containing 11700 mg/l of NaCl (0.2 mole per liter) lies beneath a one-foot lens of fresh water, which is essentially, salt free to begin with. Find the concentration of NaCl in the lens after 30 days contact. Assume a constant temperature of 15 o C. Solution: Given only diffusion mixing (no advection) The mass of dissolved NaCl is solved by Fourier series as + + × = + ..... i 25d exp 25 1 i 9d exp 9 1 i d exp ) C (C 0.811 C C o s 5 days - t (From Foundations of Environmental Engineering, Cooper, Dietz & Reinhart) also d i = diffusion coefficient; 2 i 2 i 4X t D π d × × = , where Di = Diffusivity (L 2 T -1 ) At 25 C. D i = 8×10 -10 sec m 2 = 0.0288 hr cm 2 for NaCl Temperature correction for 15 C; )] T [0.0159(T T i T i 1 2 1 2 e D D = hr cm 0.02 exp D D 2 25)] [0.0159(15 C 25 i C 15 i 0 0 = × = hence 0.05 ft cm 30.48 ft 1 4 day hrs 24 days 30 hr cm 0.02 π 4X t D π d 2 2 2 2 2 i 2 i = × × × × × = × × = since initial salt concentration in water C o = 0 and C s =11700 mg/L; applying the Fourier series we get × + × + × × = + ..... 0.05 25 exp 25 1 0.05 9 exp 9 1 0.05 exp 0) (11700 0.811 11700 C 30days C 30days L mg 1839 = NaCl
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2 2. The initial dissolved oxygen concentration of an acquiescent body of water 1-foot deep is 5.0 mg/L. Assume the rate of absorption of oxygen from the atmosphere is sufficiently fast to saturate the surface layer of the water in a relatively short period. Find the concentration after one week if the temperature of water remained constant at 15 o C.
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This note was uploaded on 01/14/2012 for the course ENV 6015 taught by Professor Taylor during the Fall '11 term at University of Central Florida.

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DIFFUSION_SOLUTION - ENV 6015 Solutions to Diffusion...

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