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Chapter 03.05Secant Method of Solving a Nonlinear Equation More ExamplesChemical Engineering

Example 1

You have a spherical storage tank containing oil. The tank has a diameter of 6 ft. You are

asked to calculate the height h to which a dipstick 8 ft long would be wet with oil when

immersed in the tank when it contains of oil.3ft4

h

r

Spherical Storage Tank

Dipstick

Figure 1 Spherical storage tank problem.

The equation that gives the height h of the liquid in the spherical tank for the given volume

and radius is given by

08197.3923

hhhfUse the secant method of finding roots of equations to find the height h to which the dipstick

is wet with oil. Conduct three iterations to estimate the root of the above equation. Find theabsolute relative approximate error at the end of each iteration and the number of significant

digits at least correct at the end of each iteration.

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Secant Method More Examples: Chemical Engineering 03.05.3

Iteration 3

The estimate of the root is

12

12223

hfhf

hhhfhh

8197.398197.398197.39

2

1

3

1

2

2

3

2

12

2

2

3

22

hhhh

hhhhh

8197.364423.0964423.08197.367185.0967185.0

64423.067185.08197.367185.0967185.067185.0

2223

23

67759.0

The absolute relative approximate error a at the end of Iteration 3 is

100

3

23

h

hha

10067759.0

67185.067759.0

%84768.0The number of significant digits at least correct is 1, because the absolute relative

approximate error is less than .%5

NONLINEAR EQUATIONS

Topic Secant Method-More ExamplesSummary Examples of Secant Method

Major Chemical Engineering

Authors Autar Kaw

Date August 7, 2009

Web Site http://numericalmethods.eng.usf.edu

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