Answer / Explanation:
Kindly note that the question is incomplete. However, kindly find the complete question below and the answer.
Complete Question
Water is flowing in a trapezoidal channel at a rate of Q=20m³/s . The critical depth y for such a channel must satisfy the equation:
0 = 1 − Q² / gA³c . B Where g= 9.81m /s² and Ac = the cross-section 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,
Answer:
Given the equation,
0 = 1 − Q² / gA³c. B
Now substituting the given value g= 9.81m /s² , Q =20m³/s, B = 3+y, and Ac = 3y+y²/2,
We get:
0 = 1 - 20² / (9.81) ( 3y + y²/2)³ (3+y)
Hence we choose f(y) = 1 - 40.7747 / (3y + y²/2)³ . (3 + y) and solve for f(y) = 0
Therefore,
To solve using a graph, we take twelve sample points ( starting at y = 0.25 in step of 0.25m and plot a graph using MS- Excel. Kindly find the graph below.
2) As evident from the sample point and the graph function f(y) gets close to zero at y = 1.5, hence the root of f(y) = 0 is Xr = 1.5
