MAT 201- Bisection Method Critical Depth in Open Channels Background: Critical d
ID: 3282484 • Letter: M
Question
MAT 201- Bisection Method Critical Depth in Open Channels Background: Critical depth plays an important role in the analysis of flow in open channels. We will look at water flowing through a trapezoidal channel at a rate of Q 20The critical depth y must satisfy the equation 0 1B where g 9.8 3 sec 2 sec2" Acthe cross-sectional area3y + B the width of the channel at the surface 3 + y 2 Assignment: Solve for critical depth y using the Bisection Method with initial guesses of a 0.5 and b-2.5. Iterate until the approximate error falls below 5% or E 0.05. How many iterations were required?Explanation / Answer
f(y)=1-400/((9.8)(3y+y2/2)3*(3+y)
Bisection method :
iteration a b (a+b)/2
1 0.500000 2.500000 1.500000
2 0.500000 1.500000 1.000000
3 0.500000 1.000000 0.750000
4 0.500000 0.750000 0.625000
5 0.500000 0.625000 0.562500
6 0.500000 0.562500 0.531250
roots of eqution is : 0.531250
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