Two tanks, each holding 100 L of liquid, are interconnected by pipes with liquid flowing from tank A into tank B at a rate of 12 L/min and from tank B into tank A at 3 L/min, as shown in the figure. Theliquid inside each tank is kept well stirred. Pure water flows into tank A at a rate of 9 L/min, and the solution flows out of tank B at 9 L/min. If, initially, tank A contains 2.6 kg of salt and tank B containsno salt (only water), determine the mass of salt in each tank at time t20. Graph on the same axes the two quantities x₁ (t) and x₂ (t), where x₁ (t) is the mass of salt in tank A and x₂ (t) is the mass intank B.Click the icon to view the figure of the tanks.XxWhat are the equations for the mass of salt in each tank at time t≥ 0?x₁ (t) =X₂ (t) =Tanks9 L/minPure waterAx₁ (t)100 Lx₁ (0)=2.6 kgPrint12 L/min←3 L/minBx2 (t)100 LX₂ (0)=0 kgDone9 L/minQ

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Answered: Two 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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A 200-liter tank initially contains 100 liters of brine solution containing 25kg of salt. A brine solution containing 0.5 kg/ liter of salt flows into the container at a rate of 1 liter/min. The solution is kept thoroughly mixed, and the mixture flows out at a rate of 0.5 liters/min. How much salt is in the container after 10 minutes? When the tank is about to overflow, another drain is opened at 1 liter/min. How much salt is in the tank when the volume returns to what it was initially?
My cat Pythagoras has purchased and installed in my back yard a large barrel with a 400-gallon capacity. It is initially half full of clean water. But he has three hoses feeding this barrel, each with a rate of flow of 2 gal./min. of water. Two provide the barrel with clean water, but the third contains a concentration of 2 g/gal. of liquid calculus text books. My other cat, Jolie, has decided to sabotage this process by puncturing a hole toward the bottom of this barrel that allows 4 gal./min. to leak. If we assume that there is a benevolent feline deity that blissfully stirs this barrel with a rather large spoon, then write a differential equation that mathematically models the rate at which the amount of liquid calculus text books changes in the barrel (at least up to the time it fills). Thereafter, solve this differential equation.
Consider a large vat containing sugar water that is to be made into soft drinks (see figure below). A B Suppose: The vat contains 230 gallons of liquid, which never changes. Sugar water with a concentration of 7 tablespoons/gallon flows through pipe A into the vat at the rate of 5 gallons/minute. • Sugar water with a concentration of 3 tablespoons/gallon flows through pipe B into the vat at the rate of 25 gallons/minute. The liquid in the vat is kept well-mixed. • Sugar water leaves the vat through pipe C at the rate of 30 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 22 tablespoons of sugar in the vat at t = 0. How many tablespoons…
A tank contains 200 gal of liquid. Initially, the tank contains pure water. At time t = 0, brine containing 3 lb/gal of salt begins to pour into the tank at a rate of 2 gal/min, and the well-stirred mixture is allowed to drain away at the same rate. How many minutes must elapse before there are 100 lb of salt in the tank?
A pasta company with a blue box produces 1,400 tons of semolina pasta per day. The pasta is fed into a machine as a large, loose dough and then squeezed through a bronze die to form a desired shape. As the pasta is squeezed through the die, the volume of space it takes up decreases while the mass remains constant, and thus the resulting shape is more dense. If m is the constant mass of the pasta in grams and V is the volume of the pasta in mL, then the density p is given by p= - m (a) If the mass remains constant while the volume changes with time, find dp dt (b) Suppose the mass of the pasta is 80g, the density is 0.8 g/mL, and the volume is decreasing at a rate of 400 mL/sec. How fast is the density of the pasta changing at that moment? mL · sec
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.
Consider the two tank apparatus shown in the figure. Each tank has capacity 500 liters and initially contains 50 liters of fresh water. At time t = 0, the well-stirred mixing process begins. Suppose that the concentration of brine flowing into Tank 1 via the top tube is 0.75 kilograms per liter, and that the flow rates are r1 = r3 = 5 liters per minute, and r2 = r4 = 12 liters per minute. (a.) Determine the volume of solution in each tank as a function of time, t, in minutes. V1(t) = ? V2(t) = ? (b) Determine the time interval of interest (The process when a tank is full or empty) Stopping time is ? minutes (c) Let Q1(t) and Q2(t) denote the amount of salt (in kilograms) in the tanks at time t (in minutes). Derive the initial value problem with Q1(t) and Q2(t) as dependent variables describing the mixing process. Enter Q1(t) as Q1(t) and Q2(t) as Q2(t) (d/dt) (Q1(t)) = ...................................................... kg/min (d/dt) (Q2(t)) =…
A solution with 35% ammonia is added at a rate of 5 liters per minute to a vat that initially contains 100 liters of pure water. The mixed solution is drained at 3 liters per minute. At what time will the solution contain 10% ammonia?

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