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moody.m

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+function moody
+%MOODY Plots the Moody chart
+%
+%   Syntax:
+%      MOODY
+%
+%   Author:
+%      Ildeberto de los Santos Ruiz
+%      [email protected]
+%
+%   References:
+%      [1] Moody, L. F. (1944), "Friction factors for pipe flow",
+%          Transactions of the ASME, 66 (8): 671–684
+
+Re = logspace(2,8,1000);
+for epsilon = [1e-5,3e-5,1e-4,3e-4,1e-3,3e-3,1e-2,3e-2]
+    loglog(Re,friction(Re,epsilon*ones(size(Re))),...
+        'LineWidth',1); hold on
+    text(1.75e7,friction(Re(end),epsilon),...
+        ['$\varepsilon=',sprintf('%7.5f',epsilon),'$'],...
+        'VerticalAlignment','bottom','Interpreter','LaTeX',...
+        'FontSize',8)
+end
+hold off
+grid on
+xlabel('Reynolds number, $\mathrm{Re}$','Interpreter','LaTeX','FontSize',10)
+ylabel('Friction factor, $f$','Interpreter','LaTeX','FontSize',10)
+ylim([0.007,0.2])
+xlim([600,1e8])
+set(gca,'TickLabelInterpreter','LaTeX','FontSize',10,...
+    'YTick',[0.007,0.01,0.02,0.03,0.05,0.07,0.1,0.2])
+hold on
+rectangle('Position',[2000,0.023,2000,0.05],'Curvature',0.5,...
+    'LineStyle','--','EdgeColor',[0.75,0.75,0.75],'FaceColor',[0.9,0.9,0.9,0.5])
+text(3000,0.08,'Critical zone','Interpreter','LaTeX',...
+    'HorizontalAlignment','center','FontSize',10)
+    function f = friction(Re,epsilon)
+        shape = size(Re);
+        Re = Re(:);
+        epsilon = epsilon(:);
+        f = zeros(size(Re));
+        for k = 1:numel(Re)
+            if Re(k) >= 3500
+                f(k) = fzero(@(f) 1/sqrt(f)+2*log10(epsilon(k)/3.7+2.51/(Re(k)*sqrt(f))),[eps,1]);
+            elseif Re(k) <= 2500
+                f(k) = 64/Re(k);
+            else
+                f(k) = NaN;
+            end
+        end
+        f = reshape(f,shape);
+    end
+end