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 arate 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 ofr 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.dQkg/mindt(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 thisequilibrium solution?7 =L/minWould 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 outflow concentration to rise towithin 1% of the desired concentration of 0.5 kilograms per liter?t =min

Let Q denotes the amount of dye in kilograms in the mixture at time t. Given information A mixing…

Answered: Consider the mixing process shown in…

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 tank originally contains 100 gal of fresh water. Then water containing lb of salt per gallon is poured into the tank at a rate of 2 gal/min, and the mixture is allowed to leave at the same rate. After 10 min the process is stopped, and fresh water is poured into the tank at a rate of 2 gal/min, with the mixture again leaving at the same rate. Find the amount of salt in the tank at the end of an additional 10 min. Round your answer to two decimal places. i 3 lbs
A tank of capacity 300 liters originally contains 80 litres of brine with 1/8 kg of salt. A mixture of 1 kg salt per liter is poured into the tank at a rate 4 liters per minute. The mixture is well stirred and allowed to leave the tank at a rate 8 liters per minute. a) Determine the amount of salt in the tank at any time. b) Determine the amount of salt in the tank at the instant when the tank begin to overflow.
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…
Najabhai
A student is concerned with the amount of air pollution students are exposed to in the school's parking lot after school. The student conducts an investigation to compare the quantity of particulate matter released from the diesel-powered buses, natural gas-powered buses, and the large and small cars as they idle waiting to pick up students. To make measurements, a small piece of white fabric is used to collect particulate matter from the tailpipe of each vehicle as it idles for five minutes. Each piece of fabric is then analyzed to measure the amount of particulate matter it collected. (i) Identify the independent variable in the investigation. (j) Identify one variable that was not mentioned in the description that could affect the results of the investigation. (k) Describe a realistic alternate sampling method to collect particulate matter from the vehicles in the investigation. (1) The student wants to ensure that the results are reliable. Explain how the student could modify the…

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