Complete using STELLA. Run the simulation until the lake reaches steady state. Also indicate the time needed to reach steady-state (99% rule is fine).

1) Nitrate MBE Problem A farmer has a 2-acre lake that was originally in a pristine condition. However, due to some new construction and lawn fertilization in a neighboring area, the runoff entering the lake is laden with nutrients. He hired an engineering firm to assess the damage from the nutrient enrichment. The engineering firm wanted to do a mass balance on nitrates. Your job is to help the engineering firm complete the mass balance given the following information: Average lake depth = 7.2 ft Initial nitrate (NO3-) concentration in the lake = 6.2 mg/L Runoff water entering the lake (nutrient rich water; assumed to be a constant flow) = 100 gallons/min Nitrates in the runoff water entering the lake = 22 mg/L Average evaporation rate from the entire lake = 1.5 L/min (assumed constant for all hours in the day) Average precipitation rate from entire lake = 2.1 L/min (rainfall converted to a continuous input) The lake has a triangular weir and discharges excess water to a neighboring stream (basically saying that excess flow entering the lake will not increase the liquid volume). Nitrate uptake by microalgae and other aquatic plants in the entire lake = 1.5 kg Nitrate/day Conversions: 1 acre = 43,560 ft?; 1 ft3 = 28.32 L = A) Write the Mass Movement and Reaction steps and develop an MBE for Nitrate concentration in the lake. Make appropriate assumptions if needed. Do a simple sketch to better understand the various terms. B) Solve the MBE and develop an equation for finding the nitrate concentration in the lake at any given time t. You need not do a derivation here. But simplify the numbers as much as you can, but without doing any integrations. Make sure you have consistent units at the end. Hints: Use volume in MBE to make units consistent. Think if rain water and evaporated water has nitrate? 1) Nitrate MBE Problem A farmer has a 2-acre lake that was originally in a pristine condition. However, due to some new construction and lawn fertilization in a neighboring area, the runoff entering the lake is laden with nutrients. He hired an engineering firm to assess the damage from the nutrient enrichment. The engineering firm wanted to do a mass balance on nitrates. Your job is to help the engineering firm complete the mass balance given the following information: Average lake depth = 7.2 ft Initial nitrate (NO3-) concentration in the lake = 6.2 mg/L Runoff water entering the lake (nutrient rich water; assumed to be a constant flow) = 100 gallons/min Nitrates in the runoff water entering the lake = 22 mg/L Average evaporation rate from the entire lake = 1.5 L/min (assumed constant for all hours in the day) Average precipitation rate from entire lake = 2.1 L/min (rainfall converted to a continuous input) The lake has a triangular weir and discharges excess water to a neighboring stream (basically saying that excess flow entering the lake will not increase the liquid volume). Nitrate uptake by microalgae and other aquatic plants in the entire lake = 1.5 kg Nitrate/day Conversions: 1 acre = 43,560 ft?; 1 ft3 = 28.32 L = A) Write the Mass Movement and Reaction steps and develop an MBE for Nitrate concentration in the lake. Make appropriate assumptions if needed. Do a simple sketch to better understand the various terms. B) Solve the MBE and develop an equation for finding the nitrate concentration in the lake at any given time t. You need not do a derivation here. But simplify the numbers as much as you can, but without doing any integrations. Make sure you have consistent units at the end. Hints: Use volume in MBE to make units consistent. Think if rain water and evaporated water has nitrate