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?
In a water bottling process, one-liter bottles are filled through a system that provides filtered water to each bottle at rate of 0.3 kg/s. How long would it take to fill a bottle? How many bottles can be filled in one hour if the system can fill 20 bottles simultaneously with a required time of 3 seconds to move away the filled bottles and bring in the new batch of empty bottles?
A device used for treating of agri-effluents has an inflow of 8 cubic feet per second and the amount of phosphorous in it is 20 milligrams per liter. The device media consists of wood and charcoal. This device eliminates 0.8 milligrams per liter of phosphorous for every 1 cubic feet of media. If the device is required to have an outflow phosphorous concentration of 0.9 milligrams per liter then find the volume of the filter media required for the device.
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
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 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
a tank in which 1 gram of chlorine is initially present in 80.38 m3 of a solution of water and chlorine. A chlorine solution concentrated at 1.49 g/m3 flows into the tank at a rate of 3 m3 /min, while the uniformly mixed solution exits the tank at 7 m3 /min. What will be the amount of chlorine present in the tank after 1 minute?
A tank initially contains 50 gal. of fresh water. Brine (water in which a certain number of pounds of salt have been dissolved), containing 2 lb/gal of salt, flows into the tank at the rate of 2 gal/min and the mixture kept uniform by stirring runs out at the same rate. How long will it take to increase from 40 lbs. to 80 lbs.?
How much water should be evaporated from 40% vlv alcohol in order to prepare 3000 mL of 60% ( v/v) alcohol?
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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