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Dialysis treatment removes urea and other waste products from a patient's blood by diverting some of the blood flow externally through a machine called a dialyzer. Assume that the dialyzer removes all of the waste products from the blood that it treats. Suppose the amount of waste product is measured n mg, a patient's blood volume is V mL, and the patient's blood is diverted through the dialyzer at rate of K mL/min. (a) Write a differential equation for the amount of waste in the blood at time t. (b) Give the units and sign of any constants appearing in your equation. (c) Draw a phase line or phase plot, find all equilibria, and classify each as unstable or locally stable. (d) Determine the limit of waste product amount as too. If this limit depends on the initial condition, describe how.

Dialysis treatment removes urea and other waste products from a patient's blood by diverting some of the blood flow externally through a machine called a dialyzer. Assume that the dialyzer removes all of the waste products from the blood that it treats. Suppose the amount of waste product is measured n mg, a patient's blood volume is V mL, and the patient's blood is diverted through the dialyzer at rate of K mL/min. (a) Write a differential equation for the amount of waste in the blood at time t. (b) Give the units and sign of any constants appearing in your equation. (c) Draw a phase line or phase plot, find all equilibria, and classify each as unstable or locally stable. (d) Determine the limit of waste product amount as too. If this limit depends on the initial condition, describe how.

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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Dialysis treatment removes urea and other waste products from a patient's blood by diverting some of the blood flow externally through a machine called a dialyzer. Assume that the dialyzer removes all of the waste products from the blood that it treats. Suppose the amount of waste product is measured in mg, a patient's blood volume is V mL, and the patient's blood is diverted through the dialyzer at a rate of K mL/min. (a) Write a differential equation for the amount of waste in the blood at time t. (b) Give the units and sign of any constants appearing in your equation. (c) Draw a phase line or phase plot, find all equilibria, and classify each as unstable or locally stable. (d) Determine the limit of waste product amount as t oo. If this limit depends on the initial condition, describe how.
Transcribed Image Text:Dialysis treatment removes urea and other waste products from a patient's blood by diverting some of the blood flow externally through a machine called a dialyzer. Assume that the dialyzer removes all of the waste products from the blood that it treats. Suppose the amount of waste product is measured in mg, a patient's blood volume is V mL, and the patient's blood is diverted through the dialyzer at a rate of K mL/min. (a) Write a differential equation for the amount of waste in the blood at time t. (b) Give the units and sign of any constants appearing in your equation. (c) Draw a phase line or phase plot, find all equilibria, and classify each as unstable or locally stable. (d) Determine the limit of waste product amount as t oo. If this limit depends on the initial condition, describe how.
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