EBK NUMERICAL METHODS FOR ENGINEERS
EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Chapter 5, Problem 16P

Water is flowing in a trapezoidal channel at a rate of Q = 20 m 3 /s . The critical depth y for such a channel must satisfy the equation

0 = 1 Q 2 g A c 3 B

where g = 9.81  m/s 2 , A c = the cross-sectional area ( m 2 ) , and B = the width of the channel at the surface ( m ) . For this case, the width and the cross-sectional area can be related to depth y by

B = 3 + y     and      A c = 3 y + y 2 2

Solve for the critical depth using (a) the graphical method, (b) bisection, and (c) false position. For (b) and (c) use initial guesses of x l = 0.5  and  x u = 2.5 , and iterate until the approximate error falls below 1% or the number of iterations exceeds 10. Discuss your results.

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EBK NUMERICAL METHODS FOR ENGINEERS

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