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By James Louis Fisher

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In other words, finding the root of f ( n) = ( ) n ( n −1) / n R −1 − 1 = 0 n −1 c Inspection of the equation indicates that singularities occur at x = 0 and 1. A plot indicates that otherwise, the function is smooth. 8518. 4 −  f   ( ∆P = f ) ρv 2 2D The six balance equations can then be solved for the 6 unknowns. The root location can be solved with a technique like the modified false position method. A bracketing method is advisable since initial guesses that bound the normal range of friction factors can be readily determined.

6 For the first series, after 25 terms are summed, the result is The results are oscillating. If carried out further to n = 39, the series will eventually converge to within 7 significant digits. In contrast the second series converges faster. It attains 7 significant digits at n = 28. 10 Solution: % % % Given: Taylor Series Approximation for cos(x) = 1 - x^2/2! + x^4/4! - ... 5 in the book), we obtain the following 1st, 2nd, 3rd, and 4th Order Taylor Series functions shown below in the Matlab program-f1, f2, f4.

X^4/4! - ... 5 in the book), we obtain the following 1st, 2nd, 3rd, and 4th Order Taylor Series functions shown below in the Matlab program-f1, f2, f4. Note the 2nd and 3rd Order Taylor Series functions are the same. From the plots below, we see that the answer is the 4th Order Taylor Series expansion. 14 Here is a VBA program to implement the Bisection function (Fig.

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