ecm 4 soln - ECM 5 Winter, 2009 Solution Set 4 1. A....

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ECM 5 Winter, 2009 Solution Set 4 1. A. Consider your own tank-draining data and use them to prepare graphs like Figures 2-3, 2-4, and 2-5. Solution : As described in chapter two, we estimate –dh/dt by making each of our data points an anchor point. That is, we determine the instantaneous change of the data by extrapolating from the average change over long time periods. Of particular note is that the shorter the time increment we use, the more inaccurate the estimate. Taking advantage of the greater stability in higher time increments, we may build lines from the two highest increments to estimate –dh/dt. Figure 1 illustrates this idea. Figure 1: an illustration of how –dh/dt is estimated We shall develop a mathematical algorithm easily applicable to our data, to aid us in streamlining the process. Consider the equation for a line: (1) b mx y + = This equation is completely specified (that is, m and b can be determined) when we have two data points. From evaluating two arbitrary increments, we get the two following equations: (2) b mx y + = 1 1 (3) b mx y + = 2 2 From figure one, we know that the intercept of the line determined by these equations is our estimate for –dh/dt. Thus, from substitution and rearrangement of equations (2) and (3), we get: (4) 2 1 1 2 2 1 x x y x y x dt dh b - - = - = 1
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ecm 4 soln - ECM 5 Winter, 2009 Solution Set 4 1. A....

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