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

HW1_5 The flow rate Qin m/s in an open channel of circular cross-section shown in the figure below is given by whereiven 8m/s is the gravitational constant and D, = (1-cost) 232D5/2 V (θ _ 0.5 sin(20))3/2 De is given by 5/2 diameter 2m diameter 4m theta Q, m/s Q, m/s 10 0.0006 0.0031 15 0.0028 0.0158 20 0.0087 0.0493 25 0.0210 0.1186 30 0.0427 0.2415 35 0.0774 0.4380 40 0.1289 0.7291 45 0.2008 1.1358 50 0.2967 1.6783 55 0.4198 2.3746 60 0.5728 3.2400 De Note that the units for θ in these equations is radians. Create at least one function handle for this equation, which has has two input, diameter dand angle θ. Use the function handles to compute flow rate Q, and print the table shown above. Note that in the table, 0 is in degrees

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.

Expert Answer

 

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

OUTPUT

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