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- 2. A large tank is partially filled with 100 gallons of fluid in which 10 pounds of salt is dissolved. Brine containing pound of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is then pumped out at a slower rate of 4 gal/min. Find the number of pounds of salt in the tank after 30 minutes.Consider two interconnected tanks as shown in the figure above. Tank 1 initial contains 100L (liters) of water and 310 g of salt, while tank 2 initially contains 100 L of water and 480 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 30 g/L of salt and is flowing at the rate of 3.5 L/min. The two connecting tubes have a flow rate of 4 L/min from tank 1 to tank 2; and of 2.5 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 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…Three tanks connected by pipes are shown on a figure below. Originally they contain 10, 20, and 40 gallons of pure water respectively. A brine with salt concentartion of 11b/gal flows into the first tank with the rate 5 gal/min and a well-mixed solution flows from the first to the second tank with the rate 8 gal/min. From the second tank the well-mixed solution flows into the third tank with the rate 8 gal/min and part of a well-mixed solution flows from the third to the first tank with the rate 3 gal/min while another part flows outside the system with the rate 5 gal/min. Write down the sys- tem of differential equations describing the amount of salt in each tank and put it into the matrix form. mixture 11b/gal flow 5 gal/min 10 gal 8 gal/min J 20 gal 3 gal/min 8 gal/min 40 gal 5 gal/min
- 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…Consider a set of 2 tanks of water with 800 gal and 500 gal in each originally; liquid enters the first tank at a rate of 15 gal/hour and exits the second tank at 15 gal/hour. Liquid flows out of tank 1 into 1. tank 2 at 20 gal/hour and back into tank 1 from tank 2 at 5 gal/hour. If the liquid entering tank 1 has 6 lb of sludge per gallon of water and each of the tanks has pure water in them to begin with, find a system of equations that models your system. (Write in matrix form but do NOT solve...)2. A tank has 72 gallons of water. Brine solution with 2lbs of salt per gallon of solution enters at a rate of 2.5 gal/min and the well-stirred mixture is also withdrawn at the same rate. When will the concentration be 0.5lb/gal of solution? 20
- Brine containing 2lbs of salt per gallon runs into a tank at 2 gal/min, brine from this tank runs into a second tank at 3 gal/min and brine runs out of the second tank at 3 gal/min. Initially, the first tank conditions 10 gal of brine with 30 lb of salt in solution and the second tank 10 gal of fresh water. Assuming uniform consideration in each tank, find the quantity of salt in the second tank at the end of 5min.3. A tank contains 80 gals. of pure water. A brine solution with 2 lbs/gal of salt enters at 2 gals/min, and the well-stirred mixture leaves at the same rate. Find (a) the amount of salt in the tank at any time O a. 80 Ibs O b. 41.3 lbs c. 23 Ibs O d. 27.73 lbsConsider two interconnected tanks of brine solution. Assume that Tank Y contains 20 litres of water and 40 grams of salt, and Tank X contains 20 litres of fresh water. Additionally, fresh water enters Tank Y at a rate of 4 litres/min, and the well-stirred solution flows from Tank Y to Tank X at a rate of 8 litres/ min. Through a different connecting pipe, the well-stirred solution in Tank X drains out at a rate of 8 litres/min, of which some flows back into Tank Y at a rate of 4 litres/min, while the remainder leaves the system. (a) Draw a diagram that depicts the flow process described above. Let Qx(t) and Qy(1), respectively, be the amount of salt in each tank at time t. Write down differential equations and initial conditions for Qx and Qy that model the flow process. (b) Is the system of differential equations homogeneous? Justify your answer. (c) Use the Laplace transform to find the amount of salt in each tank at ume r. (d) After 10 minutes, Tank X develops a leak and additional…
- 3. A 200-liter tank initially contains 100 liters of brine solution containing 25kg of salt. A brine solution containing 0.5 kg/liter of salt flows into the container at a rate of 1 liter/min. The solution is kept thoroughly mixed, and the mixture flows out at a rate of 0.5 liters/min. How much salt is in the container after 10 minutes? When the tank is about to overflow, another drain is opened at 1 liter/min. How much salt is in the tank when the volume returns to what it was initially?1. A tank contains 100 gallons of brine made by dissolving 60 pounds of salt in water. Salt water containing 1 pound of salt per gallon runs in at the rate of 2 gal/min, and the mixture, kept unifom by stirring runs out at the rate of 3 gal/min. Find the amount of salt in the tank at the end of 1 hour.Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank B at a rate of 5 L/min and from B into A at a rate of 4 L/min. The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.1 kg/L of salt flows into tank A at a rate of 10 L/min. The (diluted) solution flows out of the system from tank A at 9 L/min and from tank B at 1 L/min. If initially, tank A contains pure water and tank B contains 10 kg of salt, determine the mass of salt in each tank at time t≥0. x(t) = 10 L/min- 0.1 kg/L y(t) = 9 L/min A x(t) 100 L x(0) = 0 kg 5 L/min What is the solution to the system? 18 4 L/min B y(t) 100 L y(0) = 10 kg ..... 1 L/min O ✔