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(a) A mass balance for a pollutant in a well-mixed lake can be written as dt =W-Qc-kV√√c Given the parameter values V = 1x106 m³, Q=1x105 m³/yr, W=1x106 g/yr, and k = 0.25 m0.5/0.5/yr, use the modified secant method to solve for the steady state concentration. Employ an initial guess of c = 4 g/m³ and 8=0.5. Perform three iterations and determine the percent relative error after the third iteration. (b) The root to part (a) can be located with a fixed-point Iteration (Successive Substitution) as. c= W-Qc kV or as W-kV √c 2 One will converge with an initial guess of 2

(a) A mass balance for a pollutant in a well-mixed lake can be written as dt =W-Qc-kV√√c Given the parameter values V = 1x106 m³, Q=1x105 m³/yr, W=1x106 g/yr, and k = 0.25 m0.5/0.5/yr, use the modified secant method to solve for the steady state concentration. Employ an initial guess of c = 4 g/m³ and 8=0.5. Perform three iterations and determine the percent relative error after the third iteration. (b) The root to part (a) can be located with a fixed-point Iteration (Successive Substitution) as. c= W-Qc kV or as W-kV √c 2 One will converge with an initial guess of 2

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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(a) A mass balance for a pollutant in a well-mixed lake can be written as dt =W-Qc-kV√√c Given the parameter values V = 1x106 m³, Q=1x105 m³/yr, W=1x106 g/yr, and k = 0.25 m0.5/0.5/yr, use the modified secant method to solve for the steady state concentration. Employ an initial guess of c = 4 g/m³ and 8=0.5. Perform three iterations and determine the percent relative error after the third iteration. (b) The root to part (a) can be located with a fixed-point Iteration (Successive Substitution) as. c= W-Qc kV or as W-kV √c 2 One will converge with an initial guess of 2<c<6. Select the correct one and demonstrate why it will always work.
Transcribed Image Text:(a) A mass balance for a pollutant in a well-mixed lake can be written as dt =W-Qc-kV√√c Given the parameter values V = 1x106 m³, Q=1x105 m³/yr, W=1x106 g/yr, and k = 0.25 m0.5/0.5/yr, use the modified secant method to solve for the steady state concentration. Employ an initial guess of c = 4 g/m³ and 8=0.5. Perform three iterations and determine the percent relative error after the third iteration. (b) The root to part (a) can be located with a fixed-point Iteration (Successive Substitution) as. c= W-Qc kV or as W-kV √c 2 One will converge with an initial guess of 2<c<6. Select the correct one and demonstrate why it will always work.
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