Homework 6 Solution

Homework 6 Solution - Lecture 6 MEEN 357 Homework Solution...

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Lecture 6 MEEN 357 Homework Solution 1 Lecture-06-Homework-Solution-2009.doc RMB 1. Problem 6.15 of the textbook. You are to use the false position method. Solution : You are given the function () 21 2 cos 2 rh Vr r hr h h L r ⎛− ⎛⎞ =− ⎜⎟ ⎝⎠ (6.1) and asked to find the h when 8.5 V = , 2 r = and 5 L = . In order to put the problem into the form of finding the h that makes a function vanish, define ( ) f h by 2 cos 2 f hV r r h r h hL r −− (6.2) In order to estimate the location of the root, you need to plot (6.2). Since h is the depth of water in a pipe of diameter 2 r , the range of h is 02 . This limit was discussed when a similar formula was plotted in problem 3 of the homework for Lecture 3. Utilizing the same formal steps in that problem, the following script generates the plot of f h %Problem 6.15 Plot clc,clear all r=2 L=5 V=8.5 h=[0:.1:2*r] y=V-(r^2*acos((r-h)/r)-(r-h).*sqrt(2*r*h-h.^2))*L plot(h,y) grid on xlabel( 'h' ),ylabel( 'f(h)' ) The plot is
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Lecture 6 MEEN 357 Homework Solution 2 Lecture-06-Homework-Solution-2009.doc RMB The figure shows that the root is bracketed by [ ] 0,1 . The most direct way to generate this root is to use the function mfile falsepos.m introduced in class and the script file %Problem 6.15 by False Position Method clc,clear all r=2 L=5 V=8.5 func=@(h)(V-(r^2*acos((r-h)/r)-(r-h)*sqrt(2*r*h-h^2))*L) [root,ea,iter] = falsepos(func,0,1) The output is root = 0.7719 ea = 5.7928e-005 iter = 6
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This note was uploaded on 07/28/2010 for the course MEEN 357 taught by Professor Anamalai during the Fall '07 term at Texas A&M.

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Homework 6 Solution - Lecture 6 MEEN 357 Homework Solution...

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