Required information Water is flowing in a trapezoidal channel at a rate of Q fo

Question

Required information Water is flowing in a trapezoidal channel at a rate of Q for such a channel must satisfy the equation 20 m3/s. The critical depth y gA 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 and Solve for the critical depth of the channel using the false-position method. Use initial guesses of x 0.5 and Xu-25, and iterate until the approximate error falls below 1% or the number of iterations exceeds 0. (Round the final answer to four decimal places.) The critical depth y= | 2.4036 m.

Explanation / Answer

0 = 1 - Q^2 B / (g A^3)
1 = Q^2 B / (g A^3)
1 = 20^2 * (3+ y) /( 9.81 * (3y + y^2/2)^3)
solving we get
y = 1.51405

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