0.5 kg/L PollutantPure Water15 L/min5 L/min1000 L15 L/min1000 LPure Waterwith 5 kg pollutantTank ATank B20 L/minFor the figure shown, consider the following:• Two tanks are connected by a pipe with flow rate of 15L/min.• Tank A and Tank B each contains 1000L volume of liquid.• A pollutant with concentration of 0.5kg/L is discharged to Tank A at a rate of 15L/min, while pure water is discharged to Tank B at a rate of 5L/min.• There is an outflow of 20L/min from Tank B.• Initially, the amount of the pollutant in Tank A and in Tank B are zero and 5kg, respectively.• It is assumed that the pollutant is well mixed in each tank at any time t.Let yA(t) and yB(t) be the amount of the pollutant at any time t in Tank A and Tank B, respectively.Determine the particular solution of the corresponding system of ODES using Method of Undetermined Coefficients.What is the final equation of yA(t)?What is the final equation of yB(t)?

(1) Let be the amount of pollutants in tank A at any time .The rate of change of amount of…

Answered: 0.5 kg/L Pollutant 15 L/min 1000 L Pure…

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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4. A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held 100 L of pure water. The solution inside the tank is kept well stirred and flows out of the tank at a rate of 3 L/min. If the concentration of salt in the brine entering the tank is 0.2 kg/L, deter- mine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.1 kg/L?
Suppose: • The vat contains 270 gallons of liquid, which • • . never changes. Sugar water with a concentration of 10 tablespoons/gallon flows through pipe A into the vat at the rate of 30 gallons/minute. Sugar water with a concentration of 8 tablespoons/gallon flows through pipe B into the vat at the rate of 35 gallons/minute. • The liquid in the vat is kept well-mixed. Sugar water leaves the vat through pipe C at the rate of 65 gallons/minute. Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes. (A) Write the DE model for the time rate of change of sugar in the vat: dS dt (B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Your function will have an arbitrary constant K in it. Assume that K > 0. S(t) = (C) Suppose that there are 32 tablespoons of sugar in the vat at t = present 4 minutes later? 0. How many tablespoons will be tablespoons
A tank contains 1,000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min. Brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L/min. Let y(t) be the amount of salt (in kg) in the tank after t minutes. (a) Find the rate of change of amount of salt in the tank after t minutes. dy dt kg min How much salt is in the tank when t = 0? y(0) How much salt (in kg) is in the tank after t minutes? y = = kg (b) How much salt (in kg) is in the tank after 50 minutes? (Round the answer to one decimal place.) y(50) = kg
Let the population of living fish at time t (years) be denoted by x(t) (tonnes). An initial quantity of x0 tonnes of fish will be put into the lake at time t = 0. The net rate of change of the fish population in tonnes of fish per year is dx - = 0.5x = x² - f, x(0) = = x0 dt where xo) and f are non-negative constants and f represents the fish-harvesting rate. (a) Taking f = 0, write down the resulting differential equation stating clearly the solution method used.
A tank is initially filled with 400 gal of salt solution with a concentration of 0.08 lb/gal. At time t = 0, pure water is poured into the tank at a rate of 2 gal/min. Simultaneously, a drain is opened at the bottom of the tank allowing the solution to leave the tank at a rate of 3 gal/min. The tank is well-stirred. Let x(t) represent the amount of salt (in lb) in the tank after t min. Write down the initial value problem that x(t) satisfies. DO NOT SOLVE the initial value problem.
Can you find the amount of salt A in the tank at any time t?

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