Question 4. Consider a cascade of two tanks where V = 100 L and V, = 200 L are the volumes of the brine in the two tanks (See Figure 5.4.7 in Edward and Penny's book). The three flow rates are each 15 L/min with pure water flowing into Tank 1. Assume that each tank is stirred to have perfectly mixed brine. If Tank 1 has 16 Kilogrammes of salt and Tank 2 has 40 Kilogrammes of salt initially. (a) Find the amount z(t) of salt in Tank 1 at time t. (b) Suppose y(t) is the amount of salt in Tank 2 at time t. Derive the differential equation for Tank 2 and then solve for y(t), using the function r(t) found in part (a). (c) Finally, find the maximum amount of salt ever in Tank 2.
Question 4. Consider a cascade of two tanks where V = 100 L and V, = 200 L are the volumes of the brine in the two tanks (See Figure 5.4.7 in Edward and Penny's book). The three flow rates are each 15 L/min with pure water flowing into Tank 1. Assume that each tank is stirred to have perfectly mixed brine. If Tank 1 has 16 Kilogrammes of salt and Tank 2 has 40 Kilogrammes of salt initially. (a) Find the amount z(t) of salt in Tank 1 at time t. (b) Suppose y(t) is the amount of salt in Tank 2 at time t. Derive the differential equation for Tank 2 and then solve for y(t), using the function r(t) found in part (a). (c) Finally, find the maximum amount of salt ever in Tank 2.
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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Transcribed Image Text:Question 4. Consider a cascade of two tanks where V = 100 L and V2 = 200 L are the
volumes of the brine in the two tanks (See Figure 5.4.7 in Edward and Penny's book).
The three flow rates are each 15 L/min with pure water flowing into Tank 1. Assume
that each tank is stirred to have perfectly mixed brine. If Tank 1 has 16 Kilogrammes of
salt and Tank 2 has 40 Kilogrammes of salt initially.
(a) Find the amount r(t) of salt in Tank 1 at time t.
(b) Suppose y(t) is the amount of salt in Tank 2 at time t. Derive the differential
equation for Tank 2 and then solve for y(t), using the function r(t) found in part
(a).
(c) Finally, find the maximum amount of salt ever in Tank 2.
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