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Published byClarissa claudia Twigg Modified over 2 years ago

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Mixing problem Group 3 박재무 윤동일 장석민

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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

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Briefing conditions

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Volume – t = 0, 1000 L – Inputting = (6 L/min) – Outputting = (5 L/min) 5 L/min ※ The brine solution in the tank is kept well stirred, let’s assume the concentration of salt in the tank is uniform

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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

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Problem 1-1)

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Problem 1-1) Determine the concentration of salt in the tank as function of time Concentration = substance/volume

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Briefing conditions Volume – t = 0, 1000 L – Inputting = (6 L/min) – Outputting = (5 L/min) 5 L/min

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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 x(t) = substance In tank at time t Concentration = substance/volume

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Problem 1-1) Determine the concentration of salt in the tank as function of time Using integrating factor First linear differential equation form

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Problem 1-1) Determine the concentration of salt in the tank as function of time

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Problem 1-1) Determine the concentration of salt in the tank as function of time

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Problem 1-1) Determine the concentration of salt in the tank as function of time Concentration = substance/volume Concentration =

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Q&AQ&A

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Problem 1-2 )

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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 300min

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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 Runge Kutta order 4 300min

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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 min

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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 Method300minerror Improved Euler Size e-007 Runge Kutta order 4 Size e-009 ODE e-009 Analytic value

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Q&AQ&A

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Problem 1-3)

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Problem 1-3) Compare to example 1, what can you tell about the concentration of salt in the tank when t →∞ 5L/min

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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) = 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

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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 →∞

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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 →∞ concentration of salt(Kg/L) Time(min)Example 1Problem

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Q&AQ&A

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Thank You!

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