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1. A tank is used for chemical experiments. It initially contains 10001 of a solution with...
1. Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200...
1. Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 L of a dye solution with a concentration of 1 g/L. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 Umin, the well-stirred solution fowing out at the same rate. Find the time that wil elapse before the concentration of dye inthe tank reaches 1% of its original value.
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)
5. (20 points) A tank with a capacity of 500 liters contains 200 liters of water...
5. (20 points) A tank with a capacity of 500 liters contains 200 liters of water with 100 grams of a material in solution. Water containing a concentration of 1 g/liter of the material enters the tank at a rate of 3 liters/min, and the well-stirred mixture leaves the tank at a rate of 2 liters/min. Find the amount of mass of the material in the tank at any given time t prior to when the tank begins to overflow.
A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially hel...
A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.1 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.02 kg/L, determine the mass of salt in the tank after t min. When will the...
A brine solution of salt flows at a constant rate of 9 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.2 kg of salt. The solution inside the tank is kept...
A brine solution of salt flows at a constant rate of 9 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.2 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.04 kg/L, determine the mass of salt in the tank after t min. When will the...
3) A 200-gallon tank is half-filled with pure water. Subsequently, a salt-water solution of 3 pounds...
3) A 200-gallon tank is half-filled with pure water. Subsequently, a salt-water solution of 3 pounds per gallon enters the tank at 2 gallons per minute. Simul- taneously, the well-stirred solution leaves the tank at 6 gallons per minute. a) Write an initial value problem (IVP) that models this process. b) Solve your IVP. c) Over what time frame is the solution of your IVP valid? Explain. d) When is the amount of salt in the tank maximized? Give the...
Name Review Guide For Test 2: Covers 3.1, 4.1, 4.2, 4.3, 4.4, 4.6 1. Consider a tank used in cert...
Name Review Guide For Test 2: Covers 3.1, 4.1, 4.2, 4.3, 4.4, 4.6 1. Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200L of a dye solution with a concentration of 1 g/L. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in ata rate of 2 L/min, the well-stirred solution flowing out at the same rate. Find the time that will elapse before the concentration of...
10. Suppose a brine containing 0.2 kg of salt per liter runs into a tank initially...
10. Suppose a brine containing 0.2 kg of salt per liter runs into a tank initially filled with 500 L of water containing 5 kg of salt. The brine enters the tank at a rate of 5 L/Min. The mixture, kept uniform by stirring, is flowing out at the rate of 5 L/min. Let A(t) be the amount of salt in the tank at time t (in minutes), then set up an IVP for the scenario, then find the concentration,...
(1 point) A tank contains 50 kg of salt and 2000 L of water. A solution...
(1 point) A tank contains 50 kg of salt and 2000 L of water. A solution of a concentration 0.0125 kg of salt per liter enters a tank at the rate 7 L/min. The solution is mixed and drains from the tank at the same rate. (a) What is the concentration of our solution in the tank initially? concentration = !!! (kg/L) (b) Set up an initial value problem for the quantity y, in kg, of salt in the tank...
Salt water flows at a constant rate of 6 L/min into a tank that initially held...
Salt water flows at a constant rate of 6 L/min into a tank that initially held 100 L of salt solution in which was dissolved 0.3 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the solution entering the tank is 0.03 kg/L. a) Dtermine the mass of salt in the tank after t min. b) When will the concentration of...
1. Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 L of a dye solution with a concentration of 1 g/L. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 Umin, the well-stirred solution fowing out at the same rate. Find the time that wil elapse before the concentration of dye inthe tank reaches 1% of its original value.
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)
5. (20 points) A tank with a capacity of 500 liters contains 200 liters of water with 100 grams of a material in solution. Water containing a concentration of 1 g/liter of the material enters the tank at a rate of 3 liters/min, and the well-stirred mixture leaves the tank at a rate of 2 liters/min. Find the amount of mass of the material in the tank at any given time t prior to when the tank begins to overflow.
A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.1 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.02 kg/L, determine the mass of salt in the tank after t min. When will the...
A brine solution of salt flows at a constant rate of 9 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.2 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.04 kg/L, determine the mass of salt in the tank after t min. When will the...
3) A 200-gallon tank is half-filled with pure water. Subsequently, a salt-water solution of 3 pounds per gallon enters the tank at 2 gallons per minute. Simul- taneously, the well-stirred solution leaves the tank at 6 gallons per minute. a) Write an initial value problem (IVP) that models this process. b) Solve your IVP. c) Over what time frame is the solution of your IVP valid? Explain. d) When is the amount of salt in the tank maximized? Give the...
Name Review Guide For Test 2: Covers 3.1, 4.1, 4.2, 4.3, 4.4, 4.6 1. Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200L of a dye solution with a concentration of 1 g/L. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in ata rate of 2 L/min, the well-stirred solution flowing out at the same rate. Find the time that will elapse before the concentration of...
10. Suppose a brine containing 0.2 kg of salt per liter runs into a tank initially filled with 500 L of water containing 5 kg of salt. The brine enters the tank at a rate of 5 L/Min. The mixture, kept uniform by stirring, is flowing out at the rate of 5 L/min. Let A(t) be the amount of salt in the tank at time t (in minutes), then set up an IVP for the scenario, then find the concentration,...
(1 point) A tank contains 50 kg of salt and 2000 L of water. A solution of a concentration 0.0125 kg of salt per liter enters a tank at the rate 7 L/min. The solution is mixed and drains from the tank at the same rate. (a) What is the concentration of our solution in the tank initially? concentration = !!! (kg/L) (b) Set up an initial value problem for the quantity y, in kg, of salt in the tank...
Salt water flows at a constant rate of 6 L/min into a tank that initially held 100 L of salt solution in which was dissolved 0.3 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the solution entering the tank is 0.03 kg/L. a) Dtermine the mass of salt in the tank after t min. b) When will the concentration of...
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