mws_civ_inp_txt_direct_examples

# mws_civ_inp_txt_direct_examples - 05.02.1 Chapter 05.02...

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Unformatted text preview: 05.02.1 Chapter 05.02 Direct Method of Interpolation – More Examples Civil Engineering Example 1 To maximize a catch of bass in a lake, it is suggested to throw the line to the depth of the thermocline. The characteristic feature of this area is the sudden change in temperature. We are given the temperature vs. depth data for a lake in Table 1. Table 1 Temperature vs. depth for a lake. Temperature,   C  T Depth,   m z 19.1 0 19.1 –1 19 –2 18.8 –3 18.7 –4 18.3 –5 18.2 –6 17.6 –7 11.7 –8 9.9 –9 9.1 –10 05.02.2 Chapter 05.02 Figure 1 Temperature vs. depth of a lake. Using the given data, we see the largest change in temperature is between m 8   z and m 7   z . Determine the value of the temperature at m 5 . 7   z using the direct method of interpolation and a first order polynomial. Solution For first order polynomial interpolation (also called linear interpolation), we choose the temperature given by   z a a z T 1     , y x   1 1 , y x   x f 1 x y Direct Method of interpolation – More Examples: Civil Engineering 05.02.3 Figure 2 Linear interpolation. Since we want to find the temperature at m 5 . 7   z , and we are using a first order polynomial, we need to choose the two data points that are closest to m 5 . 7   z that also bracket m 5 . 7   z to evaluate it. The two points are 8   z and 7 1   z . Then   7 . 11 , 8    z T z   6 . 17 , 7 1 1    z T z gives     7 . 11 8 8 1      a a T     6 . 17 7 7 1      a a T Writing the equations in matrix form, we have                      6 . 17 7 . 11 7 1 8 1 1 a a Solving the above two equations gives 9 . 58  a and 9 . 5 1  a Hence   z a a z T 1     7 8 , 9 . 5 9 . 58       z z z T     5 . 7 9 . 5 9 . 58 5 . 7     T C 65 . 14   Example 2 To maximize a catch of bass in a lake, it is suggested to throw the line to the depth of the...
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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 - Tampa.

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mws_civ_inp_txt_direct_examples - 05.02.1 Chapter 05.02...

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