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## Mixing problem

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**Mixing problem**Group 3 박재무 윤동일 장석민**Contents**- Briefing conditions - Problem 1-1)Determine the function - Problem 1-2) Approximation of the concentration - Problem 1-3) Compare with example 1 and problem 1**※ The brine solution in the tank is kept well stirred,**let’s assume the concentration of salt in the tank is uniform Briefing conditions Volume – t = 0, 1000 L – Inputting = (6 L/min) – Outputting = (5 L/min) 5 L/min**Briefing conditions**Substance – t = 0, x = 0 kg –Inputting = (6 L/min)(1 kg/L) = 6 kg/min –Outputting = (5 L/min)( kg/L) = kg/min 5 L/min**Problem 1-1) Determine the concentration of salt in the**tank as function of time Concentration = substance/volume**Briefing conditions**Volume – t = 0, 1000 L – Inputting = (6 L/min) – Outputting = (5 L/min) 5 L/min**Briefing conditions**Substance – t = 0, x = 0 kg –Inputting = (6 L/min)(1 kg/L) = 6 kg/min –Outputting = (5 L/min)( kg/L) = kg/min x(t) = substance In tank at time t Concentration = substance/volume 5 L/min**Problem 1-1) Determine the concentration of salt in the**tank as function of time Using integrating factor First linear differential equation form**Problem 1-1) Determine the concentration of salt in the**tank as function of time**Problem 1-1) Determine the concentration of salt in the**tank as function of time**Problem 1-1) Determine the concentration of salt in the**tank as function of time Concentration = substance/volume Concentration =**Problem 1-2) Use the improved Euler’s method and fourth**order Runge-Kutta method to approximate the concentration of salt In the tank after 300 minutes Improved Euler’s Method**Problem 1-2) Use the improved Euler’s method and fourth**order Runge-Kutta method to approximate the concentration of salt In the tank after 300 minutes RungeKutta order 4**Problem 1-2) Use the improved Euler’s method and fourth**order Runge-Kutta method to approximate the concentration of salt In the tank after 300 minutes ODE 45**Problem 1-2) Use the improved Euler’s method and fourth**order Runge-Kutta method to approximate the concentration of salt In the tank after 300 minutes**Problem 1-3) Compare to example 1, what can you tell about**the concentration of salt in the tank when t →∞ 5L/min**Problem 1-3) Compare to example 1, what can you tell about**the concentration of salt in the tank when t →∞ exampl 1 problem 1 Volume – t = 0, 1000 L t = 0, 1000 L – Inputting = (6 L/min) Inputting = (6 L/min) – Outputting = (6 L/min) Outputting = (5 L/min) v(t) = 1000 v(t) = 1000 + t Substance – t = 0, 1000 L t = 0, 1000 L – Inputting = (6 L/min)(1 kg/L) = 6 kg/min – Outputting = (6 L/min) Outputting = (5 L/min)( kg/L) = kg/min**Problem 1-3) Compare to example 1, what can you tell about**the concentration of salt in the tank when t →∞ exampl 1 problem 1 concentration – Analytic, Both converge to 1, when t →∞**Problem 1-3) Compare to example 1, what can you tell about**the concentration of salt in the tank when t →∞ Numerically, Both also converge to 1, when t →∞