Problem:A 500 liter tank initially has 100 liters of fresh water. Salt water with a concentrationof 30g/L is added at a rate of 5 L/min while the well mixed solution is allowed to leaveat a rate of 1 L/min. This process will continue until the tank is filled. Find a functionwhich will model this system over the interval [0, t*] where t* is the time at which thetank overflows.

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Answered: Problem: A 500 liter tank initially has…

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 T1 and T2, respectively contain 200 and 100 liters of water and unspecified amounts of fertilizer. Now, set up a model describing the amount of fertilizer contained in each tank y1(t) and y2(t) at time t. please do not provide solution in image format thank you!
A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x = 3. The thermal diffusivity of the bar is k = 0.4. The bar's initial temperature f(x) = 50 degrees Celsius. The ends of the bar (x = 0 and x = 3) are then put in %3D an icy bath and kept at a constant 0 degrees C. Let u(x, t) be the temperature in the bar at x at time t, with t measured in seconds. Find u(x, t) and then U7 (2, 0.1). Put u (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.
A cylindrical tank holds 22 liters of water. At time t = 0, two taps are opened simultaneously, the upper tap that feeds the water tank with a constant speed of v1 liters per minute and the lower tap that expels the water from the tank with a constant speed of v2 liters per minute . Suppose that v1 = 11 liters / minute and v2 = 3 liters / minute. If the tank has a capacity of 75 liters, when will the tank be filled?
solve and draw a diagram of the problem Two large tanks, each holding 100L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank B at a rate of 3L/min and from tank B into tank A at a rate of 1L/min. The liquid inside each tank is kept well stirred. Pure water flows into tank A at a rate of 6L/min. The solution flows out of the system from tank A at 4L/min and from tank B at 2L/min. If, initially, tank A contains pure water and tank B contains 20kg of salt, determine the mass of salt in each tank at time t ≥ 0.
Two 100L tanks are connected in line. Saline is pumped into the first tank at a rate of 5L/min at a concentration of 2kg/L. Tank 1 is initially filled with pure water, and has an overflow drain which flows into Tank 2. Tank 2 initially contains 10kg of salt dissolved in 20L of solution, and has a drain with outflow at 5L/min. Let y(t) denote the amount of salt in Tank 1. Let x(t) denote the amount of salt in Tank 2. Determine the (two) differential equations describing the rates of change of y(t) and x(t). 5 L/min →→→ Tank 1 y(t) 100 L 5 L/min Tank 2 x(t) 100 L 5 L/min →
For a system as shown in Figure below, the tank is 5.419m radius and length is twice the radius, contain water with initial salt 200kg. fresh brinc contain (1 + cos t) kg/min of salt running in the tank at rate (50 m³/min) and the mixture kept practically uniform and runs out the tank at same rate. find the amount of salt in the tank after 1 hours.
For a redundant system with n independent identical components with constant failure rate 2, show that the MTTF is equal to (-1)'–1 nC; i i = 1 If 1= 0.01/hour, what is the minimum value of n so that the MTTF is at least 200 hours?

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