Question

Chapter 5, Problem 16P 12 Bookmarks Show all steps: OFF Problem 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 = 1-2B - ZA? 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 + Solve for the critical depth using (a) the graphical method, (b) bisection, and (c) false position. For (b) and (c) use initial guesses of xy = 0.5 and xy = 2.5, and iterate until the approximate error falls below 1% or the number of iterations exceeds 10. Discuss your results.

Please solve in MATLAB and provide screenshots of the code and a copy of the code. DO PART B ONLY.

Answer 1

>>p 1.5156 fx >> IIIIIIIIIIIIIIIIIIIIIII junk. mx + clc clear close g=9.81; Q=20; f=@ (v) 1-((Q^2* (3+y))/(g* (3*y+y^2/2)^3)); xl=0.5; xu=2.5; Applying bisection rule if f(xl) *f(xu) >0 error('Choose diffefent initial points") else p = (xl + xu)/2; err = abs(f(p)); i=0; while err > 0.01 && i<=10 if f(xl) *f(p) <0 xu = p; else xl = p; end P = (xl + xu)/2; err = abs(f(p)); i=i+1; end end

clc
clear
close
g=9.81; Q=20;
f=@(y)1-((Q^2*(3+y))/(g*(3*y+y^2/2)^3));
xl=0.5; xu=2.5;
% Applying bisection rule
if f(xl)*f(xu)>0
error('Choose diffefent initial points')
else
p = (xl + xu)/2;
err = abs(f(p));
i=0;
while err > 0.01 && i<=10
if f(xl)*f(p)<0
xu = p;
else
xl = p;
end
p = (xl + xu)/2;
err = abs(f(p));
i=i+1;
end
end

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