Q₁ (t) =Q₂ (t) =Q₁(0) =Q₂ (0) = 1.Consider two interconnected tanks as shown below. Tank 1 initially contains 600 gal ofwater with 3 lb of salt, and Tank 2 initially contains 400 gal of water with 1 lb of salt. Watercontaining 0.4 lb/gal of salt flows into Tank 1 at a rate of 3 gal/min. The well stirred mixturein Tank 1 flows into Tank 2 at a rate of 4 gal/min. The well stirred mixture in Tank 2 leavesthe tank at a rate of 6 gal/min and additionally, flows back into Tank 1 at a rate of 2 gal/min.Let Q₁(t) and Q₂(t) denote the amounts of salt (in lb) in Tank 1 and Tank 2 at time t inminutes. Let V₁ (t) and V₂(t) denote the volumes of solutions (in gal) in Tank 1 and Tank 2 attime t in minutes. Set up the initial value problem satisfied by Q₁(t) and Q₂(t) describing themixing process. (Show your work to get a full credit)Tank 172Tank 2T4

!st we will find volume of solution in both tank to find concentration of salt after t minutes and…

Answered: Consider two interconnected tanks as…

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 A and B containing 360 liters of salt solution each, are interconnected by two pipes. Pure water pours into tank A at a rate of 5 L/min. The first pipe pumps salt solution from tank B into tank A at a rate of 4 L/min. The second pipe pumps solution from tank A into tank B at a rate of 9 L/min. Finally, there is a drain on tank B from which salt solution drains at a rate of 5 L/min. Thus each tank maintains a constant volume of 360 Liters of salt solution. Initially, there is 60 kg of salt present in tank A. But tank B contains pure water. Find the amount of salt in each tank after 10 minutes. Round your answer to two decimal places.
The brine solution is recycled using a series of mixing tanks before being released outside of the tanks. Tank A receives pure water at a rate of 4 L/min. The solution is pumped to Tanks B and C at rates of 2 L/min and x L/min, respectively, from Tank A, which originally contains 500 L of brine solution in which 200 g of salt is first dissolved. At a rate of 4 L/min, Tank B from its original 400 L of brine solution in which 1000 g of salt has been dissolved pumps the solution to Tank C. At a rate of y L/min, Tank C, which originally holds 400 L of pure water, pumps the solution back to Tank B. Meanwhile, Tank C releases z L/min of solution out of the system. a. Determine the values of x, y, and z if the volume of the solution within each tank stays constant throughout time. b. Find out the brine solution's concentration coming out of each tank at time t-8 minutes. 2 L/min TANK B TANKA 4 L/min y L/min Pure water @4 L/min x L/min TANK C z L/min
A mass weighting 56 lbs stretches a spring 9 inches. The mass is in a medium that exerts a viscous resistance of A lbs when the mass has a velocity of 2 ft/sec. This system will be overdamped if A> lbs
A water well is 120 ft deep. A 120 ft cable weighing 30 lbs hangs down from the top of the well. Attached to the end of the cable is a 6 lb bucket. At the bottom of the well, the bucket initially contains 25 lbs of water. As the bucket rises at a constant rate, the water leaks out of the bucket at a constant rate such that the bucket contains 10 lbs of water the instant it reaches the top of the well. Find the work required to haul the leaky bucket up from the bottom to the top of the well.
A tank initially have 100 L with 50 g of dissolved salt. brine is pumped into the tank at a rate of 2 L/min carrying 2 grams of salt per liter. The well-stirred mixture is pumped out of the tank at a rate of 3 L/min. Find the concentration of the solution after 1 hour.
A bucket that has a mass of 30 kg when filled with sand needs to be lifted to the top of a 25 meter tall building. You have a rope that has a mass of 0.3 kg/m that must be secured to the bucket. It takes 1 meter of rope to secure the bucket. Once the bucket reaches the top of the building it only has mass 15 kg because there was a hole in the bottom and sand was leaking out at a constant rate while it was being lifted to the top of the building. Find the work done lifting the bucket (sand and rope) to the top of the building. Joules

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