Consider the two tank apparatus shown in the figure. Each tank has capacity 500 liters and initially contains 50 liters of fresh water. At time t = 0, the well-stirred mixing process begins. Suppose that the concentration of brine flowing into Tank 1 via the top tube is 0.75 kilograms per liter, and that the flow rates are r1 = r3 = 5 liters per minute, and r2 = r4 = 12 liters per minute. (a.) Determine the volume of solution in each tank as a function of time, t, in minutes. V1(t) = ? V2(t) = ? (b) Determine the time interval of interest (The process when a tank is full or empty) Stopping time is ? minutes (c) Let Q1(t) and Q2(t) denote the amount of salt (in kilograms) in the tanks at time t (in minutes). Derive the initial value problem with Q1(t) and Q2(t) as dependent variables describing the mixing process. Enter Q1(t) as Q1(t) and Q2(t) as Q2(t) (d/dt) (Q1(t)) = ...................................................... kg/min (d/dt) (Q2(t)) = .......................................................kg/min with Q1(0)=? kg and Q2(0)=? kg
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Consider the two tank apparatus shown in the figure. Each tank has capacity 500 liters and initially contains 50 liters of fresh water. At time t = 0, the well-stirred mixing process begins. Suppose that the concentration of brine flowing into Tank 1 via the top tube is 0.75 kilograms per liter, and that the flow rates are r1 = r3 = 5 liters per minute, and r2 = r4 = 12 liters per minute. (a.) Determine the volume of solution in each tank as a function of time, t, in minutes. V1(t) = ? V2(t) = ? (b) Determine the time interval of interest (The process when a tank is full or empty) Stopping time is ? minutes (c) Let Q1(t) and Q2(t) denote the amount of salt (in kilograms) in the tanks at time t (in minutes). Derive the initial value problem with Q1(t) and Q2(t) as dependent variables describing the mixing process. Enter Q1(t) as Q1(t) and Q2(t) as Q2(t) (d/dt) (Q1(t)) = ...................................................... kg/min (d/dt) (Q2(t)) = .......................................................kg/min with Q1(0)=? kg and Q2(0)=? kg |
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