# Water is flowing in a trapezoidal channel at a rate of Q = 20 m 3 /s. The critical depth

## Question:

Water is flowing in a trapezoidal channel at a rate of Q = 20 m^{3}/s. The critical depth y for such channel must satisfy the equation 0 = 1 – Q^{2}/gA^{3}_{c} B. Where g = 9.81 m/s^{2}, Ac = 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} 3y + 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_{t} = 0.5 x_{a} = 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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**Related Book For**

## Numerical Methods For Engineers

**ISBN:** 9780071244299

5th Edition

**Authors:** Steven C. Chapra, Raymond P. Canale

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