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 0 = 1 – (Q2 B)/(g Ac3) 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. Solve for the critical depth using bisection. For calculation use initial guesses of xl = 0.5 and xu = 2.5, and iterate until the approximate error falls below 3% or the number of iterations exceeds 4.

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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.