Two well-mixed tanks are interconnected. Tank A contains 60 grams of salt in 40 liters of water, and Tank Bcontains 70 grams of salt in 20 liters of water. A briny solution with concentration 2 gram/L flows into TankA at a rate of 7 L/min, while a solution with concentration 3 grams/L flows into Tank B at a rate of 5L/min. The tanks are connected, so 8 L/min flows from Tank A to Tank B, while 1 L/min flows from Tank Bto Tank A. An additional 12 L/min drains from Tank B. Letting x1 represent the grams of salt in Tank A, andx2 represent the grams of salt in Tank B, set up the IVP for amount of salt in these two tanks.x2x1(0)='23(0)=

Two well mixed tanks are interconnected. Tank A contains 60 grams of salt in 40 liters of water.Tank…

Answered: Two well-mixed tanks are…

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 tank initially contains 400 gal of water with 20 lb of salt dissolved. A brine with salt concentration 0.2 lb per gallon begins to flow in the tank at the constant rate 10 gal per minute. The completely mixed solution flows out at the same rate. Find the amount of salt in the tank after 30 minutes. How much salt would be in the tank if the flow never stopped?
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.
A sewage disposal plant has a big concrete holding tank of 800 m³ capacity. It is half full of liquid to start with and contains 25,000 kg of organic material suspended in water. Water runs into the holding tank at the rate of 125 m³/hr and the solution leaves at the rate of 100 m³/hr. How much organic material is in the tank at the end of 5 hr?
A 500 gal capacity tank initially contains 200 gal of water and 5 Ibs of salt per gallon. To reduce the concentration, water at the rate of 3 gal/min enters the tank and the thoroughly mixed solution flows out at the same rate. After 20 min. the process is stopped and brine solution flows into the tank at the same rate of 3 gal/min and at a concentration of 2 Ibs/gal. The mixed solution flows out at the rate of 2 gal/min. Find the amount of salt in the tank 30 min. after resumption of the process. O 699.79 Ib O 717.71 lb O 560.17 Ib O 913.68 Ib
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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 ✔
A water tank that initially contains 140 L of solution in which 20 g of salt was dissolved. A solution with a salt concentration of 4 g/L is added at a rate of 6 L/min. The solution is mixed well and was drained from the tank at a rate of 4 L/min. Find the answer for the following question. 1) Find the concentration of the solution in the tank after 30 minutes.
A city of 70000 residents has an average water demand of 250 L/ca.day. The institutional and commercial, and industrial average areas in the city are 250 and 350 Ha, and water demand expected is 20 and 23 m3 /Ha.d. The public water use and water unaccounted for are 10 and 6 % of total municipal water demand, respectively. Calculate total municipal demand and each component quantity as a % of total municipal demand.
A tank initially contains 100 gal of water in which is dissolved 2 lb of salt. The salt-water solution containing 1lb of salt for every 4 gal of solution enters the tank at a rate of 5 galmin. The solution leaves the tank at the same rate allowing for a constant solution volume in the tank. Determine the eventual salt content (lbs) in the tank.

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