CEE 5794: Principles John Little Problem Set #1 page:

CEE 5794: Env. Eng. Principles John LittleProblem Set #1 page: 1VIRGINIA TECHDepartment of Civil & Environmental EngineeringFall Semester, 2009Problem Set #1(1) Beginning with a mass balance about a control volume, derive the full transientsolution to the lake model outlined in class for the case with rapid exchange (i.e.,equilibrium exists) between the well-mixed water and a thin layer of well-mixedsediments. Show all your working clearly and state the principal assumptions involved.Using the data given in the table below, work the following problems:Lake volume, V 200 × 106 m3Surface area of lake, A 10 × 106 m2Throughflow of river water, Q 0.5 × 106 m3⋅d-1Constant concentration of PCE in inlet river water, Cin 5 × 10-4 g⋅m-3Constant concentration of PCE in air, y 2 × 10-6 g⋅m-3Overall mass transfer coefficient for PCE at 20oC, KOL 3 × 10-6 m⋅s-1Henry's Law constant for PCE at 20oC, m 0.5Sediment/Water partition coefficient for PCE at 20oC, Kd 10-3 m3⋅kg-1(a) Begin by neglecting the sediment interaction and assuming that the lake is initiallyfree of PCE. Plot the concentration versus time curve for the lake. Calculate the steadystatelake concentration and the time to steady-state (assume 95% of steady-state value).By comparing the magnitude of the terms in the forcing function and the time constant,determine which are the controlling phenomena.(b) Now include sediment interaction in your calculations. Assume that the sedimentoccupies 0.1% of the volume of the lake, and has a density of 2,000 kg m-3. Was itreasonable to neglect the sediment interaction for PCE? What value of Kd is required forthere to be a doubling in the time to steady-state? For this value of Kd, draw theconcentration versus time curve on the previous plot.