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MIT OpenCourseWare http://ocw.mit.edu 1.020 Ecology II: Engineering for Sustainability Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.Lectures 08_1 & 08_2 Outline: Introduction, Mass Balance, Everglades Introduction: See course information sheet Motivation/Objective: Develop a model to compute time-varying phosphorous concentrations in a stormwater detention pond. Examine effect of pond size. Approach: 1. Define system, control volume (CV), system properties, identify unknown (dissolved pond phosphorous concentration Ct at time t) 2. Write mass balance equation (incremental, over a specified time interval) 3. Relate boundary and gain/loss terms in mass balance equation to unknown Ct . 4. Specify all inputs, solve mass balance equation for unknown (MATLAB) 5. Use model to evaluate how different pond characteristics affect phosphorous concentration. Concepts and Definitions: Definitions: system, surroundings, control volume Distinguish isolated, closed, open systems Thermodynamic systems are described by bulk system properties, processes Distinguish mass inflows/outflows across CV boundary from internal gains/losses. Mass Conservation: Incremental form: lossgainoutincvMMMMMΔ−Δ+Δ−Δ=Δ over [t, t+1] Instantaneous (or rate) form: lossgainoutincvmmmmdtdM&&&&−+−= Steady-state: 0==ΔdtdMMcvcv Distinguish conservative vs non-conservative system properties. Relationship between mass and concentration: cvcvcvCVM= For Everglades example (open system): 0,,,,,1=ΔΔ=ΔΔ=ΔΔ=Δ−=Δ+ gainlosstouttinininttcvMtCMtqCMtCqMVCVCMα q = flow rate (m3 hr-1) (inflow = outflow), Cin = phopsohorous concentration in inflow Final Mass Balance Equation (expressed in terms of the unknown concentration Ct): qVCtttCCttint=Δ−Δ−+Δ=+ταττ,]1[,1= residence time , Δt = interval (hrs) between t and t+1 Model Results Note impact of pond volume and plant uptake rate on magnitude and variability of pond phosphorous


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