C Consider two interconnected tanks as shown in the figure above. Tank 1 initial contains 100 L (liters) of water and 160 g of salt, while tank 2 initially contains 60 L of water and 345 g of salt. Water containing 15 g/L of salt is poured into tank1 at a rate of 1.5 L/min while the mixture flowing into tank 2 contains a salt concentration of 50 g/L of salt and is flowing at the rate of 4 L/min. The two connecting tubes have a flow rate of 2.5 L/min from tank 1 to tank 2; and of 1 L/min from tank 2 back to tank 1. Tank 2 is drained at the rate of 5.5 L/min.
C Consider two interconnected tanks as shown in the figure above. Tank 1 initial contains 100 L (liters) of water and 160 g of salt, while tank 2 initially contains 60 L of water and 345 g of salt. Water containing 15 g/L of salt is poured into tank1 at a rate of 1.5 L/min while the mixture flowing into tank 2 contains a salt concentration of 50 g/L of salt and is flowing at the rate of 4 L/min. The two connecting tubes have a flow rate of 2.5 L/min from tank 1 to tank 2; and of 1 L/min from tank 2 back to tank 1. Tank 2 is drained at the rate of 5.5 L/min.
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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Question
![Consider two interconnected tanks as shown in the figure above. Tank 1 initial contains 100 L (liters) of water and 160 g of salt, while tank 2 initially contains 60 L of water and 345 g of salt. Water
containing 15 g/L of salt is poured into tank1 at a rate of 1.5 L/min while the mixture flowing into tank 2 contains a salt concentration of 50 g/L of salt and is flowing at the rate of 4 L/min. The two
connecting tubes have a flow rate of 2.5 L/min from tank 1 to tank 2: and of 1 L/min from tank 2 back to tank 1. Tank 2 is drained at the rate of 5.5 L/min.
You may assume that the solutions in each tank are thoroughly mixed so that the concentration of the mixture leaving any tank along any of the tubes has the same concentration of salt as the
tank as a whole. (This is not completely realistic, but as in real physics, we are going to work with the approximate, rather than exact description. The 'real' equations of physics are often too
complicated to even write down precisely, much less solve.)
How does the water in each tank change over time?
Let p(t) and g(t) be the amount of salt in g at time t in tanks 1 and 2 respectively. Write differential equations for p and q. (As usual, use the symbols p and g rather than p(t) and g(t).)
MANN
Give the initial values:
[]-[8]
=
p(0)
9(0)
Activate
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Transcribed Image Text:Consider two interconnected tanks as shown in the figure above. Tank 1 initial contains 100 L (liters) of water and 160 g of salt, while tank 2 initially contains 60 L of water and 345 g of salt. Water
containing 15 g/L of salt is poured into tank1 at a rate of 1.5 L/min while the mixture flowing into tank 2 contains a salt concentration of 50 g/L of salt and is flowing at the rate of 4 L/min. The two
connecting tubes have a flow rate of 2.5 L/min from tank 1 to tank 2: and of 1 L/min from tank 2 back to tank 1. Tank 2 is drained at the rate of 5.5 L/min.
You may assume that the solutions in each tank are thoroughly mixed so that the concentration of the mixture leaving any tank along any of the tubes has the same concentration of salt as the
tank as a whole. (This is not completely realistic, but as in real physics, we are going to work with the approximate, rather than exact description. The 'real' equations of physics are often too
complicated to even write down precisely, much less solve.)
How does the water in each tank change over time?
Let p(t) and g(t) be the amount of salt in g at time t in tanks 1 and 2 respectively. Write differential equations for p and q. (As usual, use the symbols p and g rather than p(t) and g(t).)
MANN
Give the initial values:
[]-[8]
=
p(0)
9(0)
Activate
Go to Settin
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