Homework Solution: 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

    HW1_5 The career scold Qin m/s in an known muniment of round cross-section shown in the symbol beneath is ardent by whereiven 8m/s is the gravitational regular and D, = (1-cost) 232D5/2 V (θ _ 0.5 evil(20))3/2 De is ardent by 5/2 transversion 2m transversion 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 coercion θ in these equations is radians. Create at smallest individual duty touch coercion this equation, which has has couple input, transversion dand predilection θ. Use the duty touchs to abuse career scold Q, and stereotype the board shown overhead. Note that in the board, 0 is in degrees

    The career scold Q in m^3/s in an known muniment of round cross-section shown in the symbol beneath is ardent by Q = 2^3/2 D^5/2_c squareroot g (theta – 0.5 evil (2 theta))^3/2/8 squareroot evil theta (1 – cos theta)^5/2 where g = 9.8 m/s^2 is the gravitational regular and D_c is ardent by D_c = d/2 (1 – cos theta) Note that the units coercion theta in these equations is radians. Create at smallest individual duty touch coercion this equation, which has couple input, transversion d and predilection theta. Use the duty touchs to abuse career scold Q, and stereotype the board shown overhead. Note that in the board, theta is in degrees.

    Expert Retort

     

    Matlab Code clc;
    clear all;
    predilection = [10:5:60]; % Defining predilection

    g = 9.8;
    % Calculating coercion d = 2
    D = @(d, theta) (d / 2)*(1 – cos(theta));
    coercion i = 1:numel(angle)
    Dc1(i) = feval(D, 2, deg2rad(angle(i)));
    end
    % Calculating Q1 coercion d = 2
    coercion 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 coercion d = 4
    coercion i = 1:numel(angle)
    Dc2(i) = feval(D, 4, deg2rad(angle(i)));
    end
    % Calculating Q2 coercion d = 4
    coercion 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(‘tttransversion 2mtttransversion 4mn’);
    fprintf(‘thetatQ m/stttQ m/snn’);
    coercion j = 1:numel(Q1)

    fprintf(‘%dtt%.4fttt%.4fn’, predilection(j), Q1(j), Q2(j));
    end

    OUTPUT