4 . In a trapezoidal channel, water is flowing at a rate of Q=20m³/s with a critical depth, y that satisfies the equation below: Q? B = 1 where g = 9.81m/s², Ac is the cross-sectional area in m² and B is the width in meters of the channel at the surface. The critical depth, y is related to the width and the cross sectional area using the following: B = 3+y and Ac= (6y+y²)/2 Solve for the critical depth using a. False position method. Use initial guesses of yı = 0.5 and yu = 2.5, and iterate until the approximate error falls below 1% b. Using the secant method. Use initial guesses of yn-1 = 1 and yn = 2, and iterate until the approximate error is at 0%

4 . In a trapezoidal channel, water is flowing at a rate of Q=20m³/s with a critical depth, y that satisfies the equation below: Q? B = 1 where g = 9.81m/s², Ac is the cross-sectional area in m² and B is the width in meters of the channel at the surface. The critical depth, y is related to the width and the cross sectional area using the following: B = 3+y and Ac= (6y+y²)/2 Solve for the critical depth using a. False position method. Use initial guesses of yı = 0.5 and yu = 2.5, and iterate until the approximate error falls below 1% b. Using the secant method. Use initial guesses of yn-1 = 1 and yn = 2, and iterate until the approximate error is at 0%

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

4 . In a trapezoidal channel, water is flowing at a rate of Q=20m³/s with a critical depth, y that satisfies
the equation below:
Q?
·B = 1
gA?
where g = 9.81m/s?, Ac is the cross-sectional area in m² and B is the width in meters of the channel at
the surface. The critical depth, y is related to the width and the cross sectional area using the following:
B = 3+y and Ac= (6y+y²)/2
Solve for the critical depth using
а.
False position method. Use initial guesses of yı = 0.5 and yu = 2.5, and iterate until the
approximate error falls below 1%
b.
Using the secant method. Use initial guesses of yn-1 = 1 and yn = 2, and iterate until the
approximate error is at 0%

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