A tank contains 10 Litres of water which contains 2 Kg of dissolved sugar. Water with a concentration of 1/4 Kg of sugar per Litre is pumped into the tank at a rate of 2 Litres per minute. The mixture, kept uniform by stirring, is pumped out at the same rate. i) Derive a differential equation that models the evolution of sugar at time t, x(t), using the above described dynamic process and include the initial conditions in your model. ii) Determine the amount of sugar in the tank at any point in time. iii) Does the amount of sugar in the tank, x(t), exceed 3 Kg when t ≤ 5
A tank contains 10 Litres of water which contains 2 Kg of dissolved sugar. Water with a concentration of 1/4 Kg of sugar per Litre is pumped into the tank at a rate of 2 Litres per minute. The mixture, kept uniform by stirring, is pumped out at the same rate. i) Derive a differential equation that models the evolution of sugar at time t, x(t), using the above described dynamic process and include the initial conditions in your model. ii) Determine the amount of sugar in the tank at any point in time. iii) Does the amount of sugar in the tank, x(t), exceed 3 Kg when t ≤ 5
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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A tank contains 10 Litres of water which contains 2 Kg of dissolved sugar.
Water with a concentration of 1/4 Kg of sugar per Litre is pumped into the tank at a rate of 2 Litres per minute. The mixture, kept uniform by stirring, is pumped out at the same rate.
i) Derive a differential equation that models the evolution of sugar at time t, x(t), using the above described dynamic process and include the initial conditions in your model.
ii) Determine the amount of sugar in the tank at any point in time.
iii) Does the amount of sugar in the tank, x(t), exceed 3 Kg when t ≤ 5
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