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Water is flowing in a trapezoidal channel at a rate of Q = 20 m3/s. The critical depth y for such a channel must satisfy the equation 0 = 1 – (Q2 B)/(g Ac3) where g = 9.81 m/s2, Ac = the cross-sectional area (m2), 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 Ac = 3y + y2. Solve for the critical depth using bisection. For calculation use initial guesses of xl = 0.5 and xu = 2.5, and iterate until the approximate error falls below 3% or the number of iterations exceeds 4.

Water is flowing in a trapezoidal channel at a rate of Q = 20 m3/s. The critical depth y for such a channel must satisfy the equation 0 = 1 – (Q2 B)/(g Ac3) where g = 9.81 m/s2, Ac = the cross-sectional area (m2), 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 Ac = 3y + y2. Solve for the critical depth using bisection. For calculation use initial guesses of xl = 0.5 and xu = 2.5, and iterate until the approximate error falls below 3% or the number of iterations exceeds 4.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.2: Geometric Constructions
Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...
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Water is flowing in a trapezoidal channel at a rate of Q = 20 m3/s. The critical depth y for such a channel must satisfy the equation 0 = 1 – (Q2 B)/(g Ac3) where g = 9.81 m/s2, Ac = the cross-sectional area (m2), 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 Ac = 3y + y2. Solve for the critical depth using bisection. For calculation use initial guesses of xl = 0.5 and xu = 2.5, and iterate until the approximate error falls below 3% or the number of iterations exceeds 4.

 

 
 
 
 
 
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