mws_che_nle_txt_bisection_examples

# mws_che_nle_txt_bisection_examples - Chapter 03.03...

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Chapter 03.03 Bisection Method of Solving a Nonlinear Equation – More Examples Chemical 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 4 of oil. 3 ft 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  0 8197 . 3 9 2 3 h h h f Use the bisection method of finding roots of equations to find the height, , to which the dipstick is wet with oil. Conduct three iterations to estimate the root of the above equation. h Find the absolute relative approximate error at the end of each iteration and the number of significant digits at least correct at the end of each iteration. 03.03.1

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03.03.2 Chapter 03.03 Solution From the physics of the problem, the dipstick would be wet between 0 h and , where r h 2 r radius of the tank, that is 6 0 ) 3 ( 2 0 2 0 h h r h Let us assume 6 , 0 u h h Check if the function changes sign between
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## This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida.

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mws_che_nle_txt_bisection_examples - Chapter 03.03...

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