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Water is flowing through a trapezoidal channel at a rate of Q = 20 m³/s. The critical depth y for such a channel must satisfy the equation Q² 0 = 1 - 9A where g 9.81 m/s2, Ac width and cross sectional area can be related to the depth y by = cross sectional area (m2), and B = width of the channel at the surface (m). For this case, the B = y +3 Ac = 3y + 2 Solve for the critical depth using either bisection method or regula falsi method using initial guesses of a = 0.5 and x 2.5, and iterate until the approximate error falls below 1% or the number of iterations exceeds 1000.

Water is flowing through a trapezoidal channel at a rate of Q = 20 m³/s. The critical depth y for such a channel must satisfy the equation Q² 0 = 1 - 9A where g 9.81 m/s2, Ac width and cross sectional area can be related to the depth y by = cross sectional area (m2), and B = width of the channel at the surface (m). For this case, the B = y +3 Ac = 3y + 2 Solve for the critical depth using either bisection method or regula falsi method using initial guesses of a = 0.5 and x 2.5, and iterate until the approximate error falls below 1% or the number of iterations exceeds 1000.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Practical 3: Bracketing methods Water is flowing through a trapezoidal channel at a rate of Q = 20 m³/s. The critical depth y for such a channel must satisfy the equation Q? 0 = 1 - B 9.81 m/s2, Ac cross sectional area (m2), and B width and cross sectional area can be related to the depth y by where g width of the channel at the surface (m). For this case, the B = y + 3 y? Ac = 3y + Solve for the critical depth using either bisection method or regula falsi method using initial guesses of xi Xu = 2.5, and iterate until the approximate error falls below 1% or the number of iterations exceeds 1000. 0.5 and
Transcribed Image Text:Practical 3: Bracketing methods Water is flowing through a trapezoidal channel at a rate of Q = 20 m³/s. The critical depth y for such a channel must satisfy the equation Q? 0 = 1 - B 9.81 m/s2, Ac cross sectional area (m2), and B width and cross sectional area can be related to the depth y by where g width of the channel at the surface (m). For this case, the B = y + 3 y? Ac = 3y + Solve for the critical depth using either bisection method or regula falsi method using initial guesses of xi Xu = 2.5, and iterate until the approximate error falls below 1% or the number of iterations exceeds 1000. 0.5 and
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