Environmental Systems 1 ESR 320 Problem Set 5 DUE: Friday, 11/03/2017 1. A pond

Question

Environmental Systems 1 ESR 320 Problem Set 5 DUE: Friday, 11/03/2017 1. A pond has a surface area of 0.35 ha and an average depth of 2.4 m. Three streams (A,B, C) enter the pond and one (D) leaves. The available data for flow and herbicide concentration are as follows: Stream A: Stream B: 0.75 m3/s 1.35 m'/s 16 mg/L Not Detected Stream C: 2.40 ms 23 mg/L Stream D: 4.50 m/s 3.6 mg/L There is no detectable input or output of groundwater and evaporation is balanced quite closely by precipitation. Using a mass balance state whether the herbicide appears to be degrading, and if so, state the value of the apparent first-order decay coefficient k in units of day Assume the pond is completely mixed and is at steady state. (6 pts] 2· The surface of the pond above has a temperature of 11.4 degrees Celsius. Water can be

Explanation / Answer

given

stream A, Q1 = 0.75 m^3/s

herbicide amount r1 = 16*Q1 mg m^3/Ls = 16Q1 g /s

similiarly

stream B, Q2 = 1.35 m^3/s

r2 = 0

stream C, Q3 = 2.4 m^3/s

r3 = 23Q3 g/s

stream D, Q4 = 4.5 m^3/s

r4 = 3.6Q4 g /s

hence from the given conditions

Q1 + Q2 + Q3 - Q4 = dV/dt ( V is volume of the pond) = 0

hence

Q1 + Q2 + Q3 - Q4 = 0

dV/dt = 0

now,

at time t, mass concentration of herbicide in pond = C

then amount of herbicide = CV

after time dt

amount of herbicide = CV + (r1 + r2 + r3 - r4)dt = CV + (16Q1 + 23Q3 - 3.6Q4)dt

so change in amount of herbicide = (16*0.75 + 23*2.4 - 3.6*4.5)dt = dm

dm/dt = 67 g/s = 5788.8 kg/day

hence

m = kt + C

where k is decay constant = 5788.8 kg / day

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