Wter is flowing in a trapezoidal channel at a rate of q

Question

Question: Water is flowing in a trapezoidal channel at a rate of Q = 20 m³/s. The critical depth y for such channel must satisfy the equation 0 = 1 - Q²/gA³c B. 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 + y²/2

Solve for the critical depth using

(a) The graphical method,

(b) Bisection, and

(c) False position. For (b) and (c) use initial guesses of xt = 0.5 xa = 2.5, and iterate until the approximate error falls below 1 % or the number of iterations exceeds 10. Discuss your results.