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2. A tank initially contains 120 L of pure water. A mixture containing a concentration of 7 g/L of salt enters the tank at a rate of 2 L/min, and the well-stirred mixture leaves the tank at the same rate. Find an expression in terms of y for the amount of salt in the tank at any time t. Also find the limiting amount of salt in the tank as t ∞.

2. A tank initially contains 120 L of pure water. A mixture containing a concentration of 7 g/L of salt enters the tank at a rate of 2 L/min, and the well-stirred mixture leaves the tank at the same rate. Find an expression in terms of y for the amount of salt in the tank at any time t. Also find the limiting amount of salt in the tank as t ∞.

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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acceleration during a period of a few minutes Problems 1. Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 L of a dye solution with a concentration of 1 g/L. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 L/min, the well-stirred solution flowing out at the same rate. Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value. 2. A tank initially contains 120 L of pure water. A mixture containing a concentration of 7 g/L of salt enters the tank at a rate of 2 L/min, and the well-stirred mixture leaves the tank at the same rate. Find an expression in terms of y for the amount of salt in the tank at any time t. Also find the limiting amount of salt in the tank as t →∞. 3. A tank contains 100 gal of water and 50 oz of salt. Water 1 containing a salt concentration of 1+ sin!) sint oz/gal flows into - 2 the tank at a rate of 2 gal/min, and the mixture in the tank flows out at the same rate. a. Find the amount of salt in the tank at any time. G b. Plot the solution for a time period long enough so that you see the ultimate behavior of the graph. c. The long-time behavior of the solution is an oscillation about a certain constant level. What is this level? What is the amplitude of the oscillation? 4. Suppose that a tank containing a certain liquid has an outlet near the bottom. Let h(t) be the height of the liquid surface above the outlet at time t. Torricelli's² principle states that the outflow velocity v at the outlet is equal to the velocity of a particle falling freely (with no drag) from the height h. court 2 Evangelista Torricelli (1608-1647), successor to Galileo as mathematician in Florence, published this result in 1644. In addition to this work in fluid dynamics, he is also known for constructing the first mercury barometer and for making important contributions to geometry. +4) a. Show that y gravity. b. By equating t in the tank, show where A(h) is th and a is the are coefficient that section of the C value of a for w c. Consider a- that is 3 m high and the radius c full of water, de to the level of t 5. Suppose that compounded contin a. Find the ti value as a func b. Determine c. Find the investment is 6. A young per year at an annual r continuously and th a. Determine b. Ifr = 7.5 for retirement c. If k = $2 obtained to ha 8 2/3 علك
Transcribed Image Text:acceleration during a period of a few minutes Problems 1. Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 L of a dye solution with a concentration of 1 g/L. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 L/min, the well-stirred solution flowing out at the same rate. Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value. 2. A tank initially contains 120 L of pure water. A mixture containing a concentration of 7 g/L of salt enters the tank at a rate of 2 L/min, and the well-stirred mixture leaves the tank at the same rate. Find an expression in terms of y for the amount of salt in the tank at any time t. Also find the limiting amount of salt in the tank as t →∞. 3. A tank contains 100 gal of water and 50 oz of salt. Water 1 containing a salt concentration of 1+ sin!) sint oz/gal flows into - 2 the tank at a rate of 2 gal/min, and the mixture in the tank flows out at the same rate. a. Find the amount of salt in the tank at any time. G b. Plot the solution for a time period long enough so that you see the ultimate behavior of the graph. c. The long-time behavior of the solution is an oscillation about a certain constant level. What is this level? What is the amplitude of the oscillation? 4. Suppose that a tank containing a certain liquid has an outlet near the bottom. Let h(t) be the height of the liquid surface above the outlet at time t. Torricelli's² principle states that the outflow velocity v at the outlet is equal to the velocity of a particle falling freely (with no drag) from the height h. court 2 Evangelista Torricelli (1608-1647), successor to Galileo as mathematician in Florence, published this result in 1644. In addition to this work in fluid dynamics, he is also known for constructing the first mercury barometer and for making important contributions to geometry. +4) a. Show that y gravity. b. By equating t in the tank, show where A(h) is th and a is the are coefficient that section of the C value of a for w c. Consider a- that is 3 m high and the radius c full of water, de to the level of t 5. Suppose that compounded contin a. Find the ti value as a func b. Determine c. Find the investment is 6. A young per year at an annual r continuously and th a. Determine b. Ifr = 7.5 for retirement c. If k = $2 obtained to ha 8 2/3 علك
Expert Solution
Step 1

Initial volume of water, V = 120 L

Inlet Volumetric flow rate of mixture, v0 = 2 L/min

Outlet volumetric flow rate of mixture, v0 = 2 L/min

Input Concentration of salt in mixture, Ci = γ gL

 

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