6. Tank A initially holds 500 liters ofpure water and tank B 1000 liters of90% alcohol mixture (you can thinkof it as 900 liters of alcohol mixedwith 100 liters of water). 10%mixture of alcohol enters the tank Aat a rate of 10 L/min and wellmixed solution leaves tank B withthe same rate. The water/alcohol mixture is transferred from tank A to tank B with the rate 15L/min and from tank B to tank A with the rate 5 L/min. Write the initial value problemdescribing alcohol content of each tank. Write it in the matrix form. DO NOT SOLVE.100/min of Alcohol Sclution10min Alcohol Solutionwith 10% of Alcohol concentrationTank Asonë0 % of Alcotiul50/min152/minTank B100090% of Ainahal

Let, x1(t) and x2(t) be the alcohol concentrations in tanks A and B at time t, respectively,…

Answered: 6. Tank A initially holds 500 liters 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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Consider the mixing process shown in the figure. A mixing chamber initially contains 4 liters of a clear liquid. Clear liquid flows into the chamber at a rate of 10 liters per minute. A dye solution having a concentration of 0.6 kilograms per liter is injected into the mixing chamber at a constant rate of r liters per minute. When the mixing process is started, the well-stirred mixture is pumped from the chamber at a rate of 10 + r liters per minute. (a) Develop a mathematical model for the mixing process. Let Q represent the amount of dye in kilograms in the mixture. dQ kg/min dt (b) The objective is to obtain a dye concentration in the outflow mixture of 0.5 kilograms per liter. What injection rate r is required to achieve this equilibrium solution? 7 = L/min Would this equilibrium value of r be different if the fluid in the chamber at time t = 0 contained some dye? no (c) Assume the mixing chamber contains 4 liters of clear liquid at time t = 0. How many minutes will it take for the…
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
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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!
Solve number 4
5. A fluid initially at 100°C is placed outside on a day when the temperature is -10°C, and the temper- ature of the fluid drops by 20°C in one minute. When the temperature will drop to 0°C?
6. A 50 gallons tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 lb of salt per gallon is poured into the tank at the rate of 4 gal/min, while the well-stirred mixture leaves the tank at the rate of 2 gal/min. Find a. the amount of time required for overflow to occur b. the amount of salt in the tank at the moment of overflow

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