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Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Current Attempt in Progress Consider the two interconnected tanks shown in the following figure, where vị = 2, v2 = 0.5, v12 = 4, v21 = 2, v20 = 2.5. %3D %3D V galmin V2 gavmin 1 oz/gal 3 oz/gal Pi2 gavmin Q,(t) oz salt jes zo (3)°D V218almin Tank 1 Tank 2 Van gal/min 20 Tank 1 initially contains 32 gal of water and 25 oz of salt, and Tank 2 initially contains 56 gal of water and 15 oz of salt. Water containing 1 oz/gal of salt flows into Tank 1 at a rate of 2 gal/min. The mixture flows from Tank 1 to Tank 2 at a rate of 4 gal/min. Water containing 3 oz/gal of salt also flows into Tank 2 at a rate of 0.5 gal/min (from the outside). The mixture drains from Tank 2 at a rate of 4.5 gal/min, of which some flows back into Tank 1 at a rate of 2 gal/min, while the remainder leaves the system. Let Q (t) and Q, (t), respectively, be the amount of salt in each tank at time t. Write down differential equations and initial conditions that model the flow process. Observethat the system of differential equations is nonhomogeneous. Find the values of Q and O, for which the system is in equilibrium, that is, does not change with time. Let QF and O be the equilibrium values.
Transcribed Image Text:Current Attempt in Progress Consider the two interconnected tanks shown in the following figure, where vị = 2, v2 = 0.5, v12 = 4, v21 = 2, v20 = 2.5. %3D %3D V galmin V2 gavmin 1 oz/gal 3 oz/gal Pi2 gavmin Q,(t) oz salt jes zo (3)°D V218almin Tank 1 Tank 2 Van gal/min 20 Tank 1 initially contains 32 gal of water and 25 oz of salt, and Tank 2 initially contains 56 gal of water and 15 oz of salt. Water containing 1 oz/gal of salt flows into Tank 1 at a rate of 2 gal/min. The mixture flows from Tank 1 to Tank 2 at a rate of 4 gal/min. Water containing 3 oz/gal of salt also flows into Tank 2 at a rate of 0.5 gal/min (from the outside). The mixture drains from Tank 2 at a rate of 4.5 gal/min, of which some flows back into Tank 1 at a rate of 2 gal/min, while the remainder leaves the system. Let Q (t) and Q, (t), respectively, be the amount of salt in each tank at time t. Write down differential equations and initial conditions that model the flow process. Observethat the system of differential equations is nonhomogeneous. Find the values of Q and O, for which the system is in equilibrium, that is, does not change with time. Let QF and O be the equilibrium values.
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