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.
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.
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.
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 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
A technician is changing a automotbile's transmission fluid. The manual tells him the transmission hold 7.8 quarts of fluid. When He drains the transmission, it only releases 3.1 quarts. He closes the plug and puts 3.1 quarts of fresh fluid back in. The manual tells him to run the car for 10 minutes to completely mix the fresh fluid in. The manual states to repeat this process 2 more times. Knowing that some fresh fluid is lost on each of the following 2 drains, what is the final ratio of fresh fluid to old?
H.W. 1) Calculate the volume of cylinder has 15 m height and 8 m diameter. 2) If we have other cylinder with the same height but it volume greater than first cylinder by 20%, how long its radius? 3) Write a program to calculate the volumetric and mass flow rate of a liquid flowing in a pipe with a velocity equal to 0.5 m/s. Knowing that the diameter of this pipe is 0.1 m and the density of this liquid is 890 kg/m³ ? 4) For the following distillation column write a code to find the value of stream B and the compositions of stream D? D=80 X% ? S%? T%? Z% ? F=100kg 15% X 25% S 40% T 20% Z B=? 15% X 25% S 40% T 20% Z 9 5) Compute the reaction rate constant for a first-order reaction given by the -E/RT Arrhenius law k = A e at a temperature T = 500 K. Here the activation energy is E=20 kcal/mol and the pre-exponential factor is A=10¹3 s¹. The ideal gas constant is R=1.987 cal/mol K.

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