Water is flowing in a trapezoidal channel at a rate of Q = 20 m3/s. The critical depth y f...

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

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

Solve for the critical depth using (a) the graphical method, (b) bisection, and (c) false position. For (b) and (c) use initial guesses of xl = 0.5 and xu = 2.5, and iterate until the approximate error falls below 1% or the number of iterations exceeds 10. Discuss your results.