mws_che_dif_discrete_examples

mws_che_dif_discrete_examples - Chapter 02.03...

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Chapter 02.03 Differentiation of Discrete Functions-More Examples Chemical Engineering Example 1 A new fuel for recreational boats being developed at the local university was tested at an area pond by a team of engineers. Their interest is to document the environmental impact of the fuel – how quickly does the slick spread? Table 1 shows the video camera record of the radius of the wave generated by a drop of the fuel that fell into the pond. Using the data, (a) Compute the rate at which the radius of the drop was changing at 2 t seconds. (b) Estimate the rate at which the area of the contaminant was spreading across the pond at 2 t seconds. Table 1 Radius as a function of time. Time,  s t 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Radius,  m R 0 0.236 0.667 1.225 1.886 2.635 3.464 4.365 5.333 Use the forward divided difference approximation of the first derivative to solve the above problem. Use a time step of 0.5 seconds. Solution (a)    t t R t R t R i i i 1 2 i t 5 . 2 1 i t 5 . 0 2 5 . 2 1 i i t t t   5 . 0 2 5 . 2 2 R R R 5 . 0 886 . 1 635 . 2 m/s 498 . 1 (b) 2 Area R
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02.03.2 Chapter 02.03 Time,  s t 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Area,   2 m A 0 0.17497 1.3977 4.7144 11.175 21.813 37.697 59.857 89.350    t t A t A t A i i i 1 2 i t 5 . 2 1 i t 5 . 0 2 5 . 2 1 i i t t t    5 . 0 2 5 . 2 10 A A A 5 . 0 175 . 11 813 . 21 s / m 276 . 21 2 Example 2 A new fuel for recreational boats being developed at the local university was tested at an area pond by a team of engineers. Their interest is to document the environmental impact of the fuel – how quickly does the slick spread? Table 2 shows the video camera record of the radius of the wave generated by a drop of the fuel that fell into the pond. Using the data, (a) Compute the rate at which the radius of the drop was changing at 2 t seconds. (b) Estimate the rate at which the area of the contaminant was spreading across the pond at 2 t seconds. Table 2 Radius as a function of time. Time,  s t 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Radius,  m R 0 0.236 0.667 1.225 1.886 2.635 3.464 4.365 5.333 Use a third order polynomial interpolant for the radius and area calculations.
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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_dif_discrete_examples - Chapter 02.03...

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