4. Suppose there are two tanks, each containing 200 l of fluid. Tank 1 initially contains...
4. Suppose there are two tanks, each containing 200 l of fluid. Tank 1 initially contains pure water and tank 2 initially contains water with 200 kg of salt dissolved. The tanks are stirred constantly so their solutions have uniform concentration. There is a pipe which takes 10 l/min from tank 1 to tank 2, and another pipe which takes 5 l/min from tank 2 to tank 1. Also, pure water is being pumped into tank 1 at a rate of 10 l/min, and solution is being removed at a rate of 5 l/min from each of tank 1 and tank 2. Find the amount of salt in tank 2 after 30 minutes.
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4. Suppose there are two tanks, each containing 200 l of fluid.
Tank 1 initially contains...
15. Consider a two tank system pictured below. Suppose tank A contains 100 gallons of water in which 120 pounds of salt are dissolved initially. Suppose tank B has 100 gallons of water in which zero...
15. Consider a two tank system pictured below. Suppose tank A contains 100 gallons of water in which 120 pounds of salt are dissolved initially. Suppose tank B has 100 gallons of water in which zero pounds of salt are dissolved initially. Liquid is pumped into and out of the tanks as indicated in the figure; the mixture exchanged between the two tanks and the liquid pumped out of tank B are assumed to be well mixed. How many pounds...
A tank initially contains 120 L of pure water. A salt mixture containing a concentration of...
A tank initially contains 120 L of pure water. A salt mixture containing a concentration of 1.5 g/L enters the tank at a rate of 2 L/min, and the well-stirred mixture leaves the tank at the same rate. Find an expression for the amount of salt in the tank at any time t. Also, find the limiting amount of salt in the tank as t +0. (10 points)
11. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved....
11. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 4 L/min. The well-mixed solution is pumped out at the same rate. Find the number of grams of salt in the tank at time t.
6. A 500 L tank initially contains 10 g of salt dissolved in 200 L of...
6. A 500 L tank initially contains 10 g of salt dissolved in 200 L of water. Water containing 1/4 g of salt per liter is poured into the tank at the rate of 4 L/min and the mixture is drained from the tank at the rate of 2 L/min. Find an initial value problem that solve for x(t), the mass of salt in the tank at time t prior to when the tank overflows, then solve for x(t).
Consider two tanks A (with 45 L of solution) and B (with 55 L of solution) in a dynamic fluid system. Water is flowing...
Consider two tanks A (with 45 L of solution) and B (with 55 L of solution) in a dynamic fluid system. Water is flowing into tank A at a rate of 330 L/hr Water is flowing into tank B at a rate of 370 L/hr. Fluid is pumped from tank A to tank B at a rate of 180 L/hr and fluid is pumped from tank B to tank A at a rate of 165 L/hr. Fluid is pumped out...
I just need help understand where I get the 7 for the dx/dt 1. (5 points) Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from Tank A into Tank B at...
I just need help understand
where I get the 7 for the dx/dt
1. (5 points) 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 3 L/min and from B into A at a rate of 1 L/min. The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into Tank A...
Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowi...
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 4 Umin and from B into A at a rate of 1 L/min The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of 8 L/min. The (diluted) solution flows out of the system from tank...
Water 12 L/min Mixture 4 L/min 100 L 100 L Mixture 16 L/min Mixture 12 L/min Mixing tank A holds ...
Water 12 L/min Mixture 4 L/min 100 L 100 L Mixture 16 L/min Mixture 12 L/min Mixing tank A holds 100 L of water in which 0.04 kg of salts is dissolved. Suppose tank B contains 100 L of water which has 0.02 kg of salt. Liquid is pumped in and out of the tanks as indicated in the figure. The mixture exchanged between the two tanks and the liquid pumped out of tank B is assumed to be well...
Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid...
Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank Bat a rate of 4 min and from B into A at a rate of 2 Limin The liquid inside each tank is kept wel stirred. A brine solution with a concentration of 0.2 ko'l of salt flows into tank Aata rate of Limin. The (diluted) solution flows out of the system from tank Aat 6 min and...
*Using Differential Equations 3. A solution containing 0.2 kg/l of salt is pumped into a tank...
*Using Differential
Equations
3. A solution containing 0.2 kg/l of salt is pumped into a tank containing 51 of pure water at a rate of 317 min. If the well stirred mixture is pumped from the tank at the same rate of 31/min, how long does it take in minutes for the liquid in the tank to contain 0.5 kg of salt?
15. Consider a two tank system pictured below. Suppose tank A contains 100 gallons of water in which 120 pounds of salt are dissolved initially. Suppose tank B has 100 gallons of water in which zero pounds of salt are dissolved initially. Liquid is pumped into and out of the tanks as indicated in the figure; the mixture exchanged between the two tanks and the liquid pumped out of tank B are assumed to be well mixed. How many pounds...
A tank initially contains 120 L of pure water. A salt mixture containing a concentration of 1.5 g/L enters the tank at a rate of 2 L/min, and the well-stirred mixture leaves the tank at the same rate. Find an expression for the amount of salt in the tank at any time t. Also, find the limiting amount of salt in the tank as t +0. (10 points)
11. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 4 L/min. The well-mixed solution is pumped out at the same rate. Find the number of grams of salt in the tank at time t.
6. A 500 L tank initially contains 10 g of salt dissolved in 200 L of water. Water containing 1/4 g of salt per liter is poured into the tank at the rate of 4 L/min and the mixture is drained from the tank at the rate of 2 L/min. Find an initial value problem that solve for x(t), the mass of salt in the tank at time t prior to when the tank overflows, then solve for x(t).
Consider two tanks A (with 45 L of solution) and B (with 55 L of solution) in a dynamic fluid system. Water is flowing into tank A at a rate of 330 L/hr Water is flowing into tank B at a rate of 370 L/hr. Fluid is pumped from tank A to tank B at a rate of 180 L/hr and fluid is pumped from tank B to tank A at a rate of 165 L/hr. Fluid is pumped out...
I just need help understand
where I get the 7 for the dx/dt
1. (5 points) 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 3 L/min and from B into A at a rate of 1 L/min. The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into Tank A...
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 4 Umin and from B into A at a rate of 1 L/min The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of 8 L/min. The (diluted) solution flows out of the system from tank...
Water 12 L/min Mixture 4 L/min 100 L 100 L Mixture 16 L/min Mixture 12 L/min Mixing tank A holds 100 L of water in which 0.04 kg of salts is dissolved. Suppose tank B contains 100 L of water which has 0.02 kg of salt. Liquid is pumped in and out of the tanks as indicated in the figure. The mixture exchanged between the two tanks and the liquid pumped out of tank B is assumed to be well...
Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank Bat a rate of 4 min and from B into A at a rate of 2 Limin The liquid inside each tank is kept wel stirred. A brine solution with a concentration of 0.2 ko'l of salt flows into tank Aata rate of Limin. The (diluted) solution flows out of the system from tank Aat 6 min and...
*Using Differential
Equations
3. A solution containing 0.2 kg/l of salt is pumped into a tank containing 51 of pure water at a rate of 317 min. If the well stirred mixture is pumped from the tank at the same rate of 31/min, how long does it take in minutes for the liquid in the tank to contain 0.5 kg of salt?
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