Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank B at arate of 4 L/min and from B into A at a rate of 3 L/min. The liquid inside each tank is kept well stirred. A brine solution with aconcentration 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 tankA at 7 L/min and from tank B at 1 L/min. If initially, tank A contains pure water and tank B contains 20 kg of salt, determinethe mass of salt in each tank at time t≥ 0.AB8 L/min4 L/min0.2 kg/Lx(t)100 Lx(0) 0 kgy(t)100 Ly(0) = 20 kg7 L/min1 L/min3 L/minWhat is the solution to the system?x(t) =y(t)=

Let x(t) kg and y(t) kg be the salt mass in tanks A and B respectively.For tank A:Given that the…

Answered: Two large tanks, each holding 100 L of…

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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Two tanks are interconnected. Tank A contains 70 grams of salt in 50 liters of water, and Tank B contains 80 grams of salt in 20 liters of water. A solution of 4 gram/L flows into Tank A at a rate of 5 L/min, while a solution of 1 grams/L flows into Tank B at a rate of 10 L/min. The tanks are well mixed. The tanks are connected, so 6 L/min flows from Tank A to Tank B, while 1 L/min flows from Tank B to Tank A. An additional 15 L/min drains from Tank B. Letting a represent the grams of salt in Tank A, and y represent the grams of salt in Tank B, set up the system of differential equations for these two tanks. dx dt dy dt x (0) = 11 2 y(0) =
A cylindrical container, 80 cm in diameter is initially filled with water to a depth of 119.367 cm. Then 0.05 kilograms of salt are dissolved in the tank. Brine containing 2 grams of salt per liter is then pumped into the tank at the rate of 0.006 m3 per minute and the solution mixed well is pumped out of the same rate. Find:a. The number of grams of salt in the tank at any time (in minutes)b. The amount of salt(grams) in the tank after 8 minutes. c. The time when the amount of salt in the tank is 200 grams.
Two well-mixed tanks are interconnected. Tank A contains 60 grams of salt in 40 liters of water, and Tank B contains 70 grams of salt in 20 liters of water. A briny solution with concentration 2 gram/L flows into Tank A at a rate of 7 L/min, while a solution with concentration 3 grams/L flows into Tank B at a rate of 5 L/min. The tanks are connected, so 8 L/min flows from Tank A to Tank B, while 1 L/min flows from Tank B to Tank A. An additional 12 L/min drains from Tank B. Letting x1 represent the grams of salt in Tank A, and x2 represent the grams of salt in Tank B, set up the IVP for amount of salt in these two tanks. x2 x1(0) = ' 23(0) =
A tank initially contains 100 L of fresh water. Solution 1 is a brine solution containing 3 kg of salt per L and is allowed to enter the tank at a rate of 2 L/min. Solution 2 is a brine solution containing 2 kg of salt per L and is allowed to enter the tank at a rate of 1 L/min. The well-stirred mixture flows out of the tank at the rate of 4 L/min. Determine the amount of salt (in kg) in the tank after one hour. Round your answer into two (2) decimal places. A. 88.94 kg B. 48.94 kg C. 48.49 kg D. 99.84 kg
A tank contains 100 liters of brine, with 50 kg total dissolved salt. Saltwater, with a concentration of 0.5 kg per liter, is allowed to run into the tank at the rate of 3 liters a minute. Brine run out of the tank at the rate of 2 liters a minute. The instantaneous concentration in the tank is kept uniform by stirring. How much salt is in the tank at the end of one hour?
In a certain resort with a swimming pool having a volume of 10,000 gallons, the pool water has a 0.01% chlorine concentration. The city water district started pumping water to the pool with concentration 0.001% at a rate of 5 gal/min. Water is flowing out of the pool also at the same rate. Chlorine concentration is the pool is considered safe if it does not exceed 0.0099%. In an hour of continuous pumping, would the chlorine concentration in the pool still be safe for use? Select the correct response: Cannot be determined. none of these It will still be safe for use. Swimming must not be allowed after one hour.
For an auditorium: Room condition: 26oC DPT, 19 oC WPT; Outside conditions: 35 oC DPT 27 oC WPT; Room heat gains: Sensible heat= 11.1 kW Latent Heat= 3.9 kW The conditioned air supplied to the room is 50 cm/min and contains 25 percent fresh air and 75 percent re-circulated room air. Determine; a) The DBT and WBT of supply air. b) The DBT and WBT of mixed fresh and re-circulated air before the cooling coil. c) The apparatus due point in bypass factor of the coil d) The refrigeration load on the cooling coil and the moisture removed by the coil.
A pond initially contains 1M gal of water and an unknown amount of an undesirable chemical. Water containing 0.01 gram of this chemical per gallon flows into the pond at a rate of 300 gal/hr. The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. How many days elapsed when the amount of chemical in the pond became 2,300 grams from an amount of 100 grams? 40.2 days O 34.9 days O 29.6 days 38.7 days
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
A cylindrical container, 80 cm in diameter is initially filled with water to a depth of 119.367 cm. Then 0.05 kilograms of salt are dissolved in the tank. Brine containing 2 grams of salt per liter is then pumped into the tank at the rate of 0.006 m³ per minute and the solution mixed well is pumped out of the same rate. Find: a. The number of grams of salt in the tank at any time (in minutes) b. The amount of salt(grams) in the tank after 8 minutes. c. The time when the amount of salt in the tank is 200 grams.
What geometric transformation of 3D space happens in this matrix-vector multiplication? 010 -1 0 0 0 01 9).( (3) Please note: All rotation directions to be understood as when looking along the rotation axis towards the origin. O Clockwise rotation by 90 degrees around the x3 axis Counter-clockwise rotation by 90 degrees around the x3 axis Clockwise rotation by 90 degrees around the x₂ axis Counter-clockwise rotation by 90 degrees around the x2 axis O Clockwise rotation by 90 degrees around the x₁ axis Counter-clockwise rotation by 90 degrees around the x₁ axis O Mirroring across the x₁-x2 plane Mirroring across the x₁-x3 plane Mirroring across the X₂-X3 plane
A tank originally contains 100 gal of fresh water. Then water containing lb of salt per gallon is poured into the tank at a rate of 2 gal/min, and the mixture is allowed to leave at the same rate. After 10 min the process is stopped, and fresh water is poured into the tank at a rate of 2 gal/min, with the mixture again leaving at the same rate. Find the amount of salt in the tank at the end of an additional 10 min. Round your answer to two decimal places. i 3 lbs

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