A mass balance for pollutant in a well-mixed lake can be given as follows: de = M - Fc - kvVe dt Given volume v =1x10ʻ m', volumetric flow rate F =1x10° m/hr, mass flow rate M =1x10 g/hr and k = 0.2 m0/go.5/hr. a) Estimate the steady state concentration using the modified secant method. Employ an initial guess of c = 3 g/m and ô = 0.5. The acceptable approximate percentage error must be less than 0.5%. Perform the calculation up to 4 decimal points. b) The steady state concentration also can be estimated with fixed-point method as follows: (M-Fc M - kvve or as kV F Between these two equations, identify which one will converge for initial guess of c = 3 g/m. Perform three iterations only and determine the approximate percentage error.

A mass balance for pollutant in a well-mixed lake can be given as follows: de = M - Fc - kvVe dt Given volume v =1x10ʻ m', volumetric flow rate F =1x10° m/hr, mass flow rate M =1x10 g/hr and k = 0.2 m0/go.5/hr. a) Estimate the steady state concentration using the modified secant method. Employ an initial guess of c = 3 g/m and ô = 0.5. The acceptable approximate percentage error must be less than 0.5%. Perform the calculation up to 4 decimal points. b) The steady state concentration also can be estimated with fixed-point method as follows: (M-Fc M - kvve or as kV F Between these two equations, identify which one will converge for initial guess of c = 3 g/m. Perform three iterations only and determine the approximate percentage error.

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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Question

A mass balance for pollutant in a well-mixed lake can be given as follows:
de
V
= M – Fc – kVc
dt
Given volume v =1x10ʻ m, volumetric flow rate F =1x10° m/hr, mass flow rate M =1x10
g/hr and k = 0.2 m05/g.5/hr.
a) Estimate the steady state concentration using the modified secant method. Employ an
initial guess of c = 3 g/m and & = 0.5. The acceptable approximate percentage error must
be less than 0.5%. Perform the calculation up to 4 decimal points.
b) The steady state concentration also can be estimated with fixed-point method as follows:
M- Fc
C =
M – kvve
C =
or as
kV
F
Between these two equations, identify which one will converge for initial guess of c = 3
g/m. Perform three iterations only and determine the approximate percentage error.

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