Consider two interconnected tanks as shown in the figure above. Tank 1 initial c
ID: 2850337 • Letter: C
Question
Consider two interconnected tanks as shown in the figure above. Tank 1 initial contains 100 L (liters) of water and 375 g of salt, while tank 2 initially contains 80 L of water and 405 g of salt. Water containing 45 g/L of salt is poured into tank 1 at a rate of 1.5 L/min while the mixture flowing into tank 2 contains a salt concentration of 40 g/L of salt and is flowing at the rate of 3.5 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 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 arc 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 q(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 q rather than p(t) and q(t ).) Give the initial values: Show the equation that needs to be solved to find a constant solution to the differential equation: A constant solution is obtained if p (t) = for all time t and q(t) = for all time t.Explanation / Answer
'