# Answered Essay: The flow rate Q in m^3/s in an open channel of circular cross-section shown in the figure below is given by Q = 2^3/2

The flow rate Q in m^3/s in an open channel of circular cross-section shown in the figure below is given by Q = 2^3/2 D^5/2_c squareroot g (theta – 0.5 sin (2 theta))^3/2/8 squareroot sin theta (1 – cos theta)^5/2 where g = 9.8 m/s^2 is the gravitational constant and D_c is given by D_c = d/2 (1 – cos theta) Note that the units for theta in these equations is radians. Create at least one function handle for this equation, which has two input, diameter d and angle theta. Use the function handles to compute flow rate Q, and print the table shown above. Note that in the table, theta is in degrees.

 Matlab Code clc; clear all; angle = [10:5:60]; % Defining angle g = 9.8; % Calculating for d = 2 D = @(d, theta) (d / 2)*(1 – cos(theta)); for i = 1:numel(angle) Dc1(i) = feval(D, 2, deg2rad(angle(i))); end % Calculating Q1 for d = 2 for i = 1:numel(Dc1) Q1(i) = (2^(3/2)*Dc1(i)^(5/2)*sqrt(g).*(deg2rad(angle(i)) … – 0.5.*sin(2*deg2rad(angle(i)))).^(3/2) ) / … ( 8*sqrt(sin(deg2rad(angle(i)))).*((1 – cos(deg2rad(angle(i)))).^(5 / 2)) ); end % Calculating for d = 4 for i = 1:numel(angle) Dc2(i) = feval(D, 4, deg2rad(angle(i))); end % Calculating Q2 for d = 4 for i = 1:numel(Dc2) Q2(i) = (2^(3/2)*Dc2(i)^(5/2)*sqrt(g).*(deg2rad(angle(i)) … – 0.5.*sin(2*deg2rad(angle(i)))).^(3/2) ) / … ( 8*sqrt(sin(deg2rad(angle(i)))).*((1 – cos(deg2rad(angle(i)))).^(5 / 2)) ); end fprintf(‘ttdiameter 2mttdiameter 4mn’); fprintf(‘thetatQ m/stttQ m/snn’); for j = 1:numel(Q1) fprintf(‘%dtt%.4fttt%.4fn’, angle(j), Q1(j), Q2(j)); end

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