PS7_solution

# 4 cpmlcp0sqrt1 m2m21gamma 12m2 2sqrt1 m2cp0 display

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Unformatted text preview: sqrt(1-M^2))*Cp_0); %Display peak negative Cp value from each of the rules disp(['M=' num2str(M)]) disp(['Minimum pressure coefficient from the Prandtl-Glauert,' ... 'Karman-Tsien and Laitone compressibility rules']) disp([min(Cp_M_PG) min(Cp_M_KT) min(Cp_M_L)]) %PLot the compressible pressure coefficient along the airfoil surface figure(i+1) plot(naca0012_x,Cp_M_PG,naca0012_x,Cp_M_KT,naca0012_x,Cp_M_L) legend('Cp_PG','Cp_KT','Cp_L') title(['M=' num2str(M)]) set(gca,'YDir','reverse') ylabel('Cp') xlabel('x') axis([0 1 -1 1]) end %Solve for the critical Mach number Cpmin=min(Cp_0); %Peak negative incompressible pressure coefficient %%Prandtl Glauert Mcr_PG=fzero(@(Mcr) Cpmin/sqrt(1-Mcr^2) - 2/(gamma * Mcr^2)... *(((1+(gamma-1)*0.5*Mcr^2)/(1+(gamma-1)/2))^(gamma/(gamma-1))-1),0.5); %%Karman Tsien Mcr_KT=fzero(@(Mcr) Cpmin/(sqrt(1-Mcr^2)+Mcr^2/... (1+sqrt(1-Mcr^2))*Cpmin/2)- 2/(gamma * Mcr^2)... *(((1+(gamma-1)*0.5*Mcr^2)/(1+(gamma-1)/2))^(gamma/(gamma-1))-1),0.5); %%Laitone's rule Mcr_L=fzero(@(Mcr) Cpmin/(sqrt(1-Mcr^2)+Mcr^2*(1+(gamma-1)/2*Mcr^2)... /(2*sqrt(1-Mcr^2))*Cpmin) - 2/(gamma * Mcr^2)... *(((1+(gamma-1)*0.5*Mcr^2)/(1+(gamma-1)/2))^(gamma/(gamma-1))-1),0.5); disp(['Critical Mach number as determined from the Prandtl-Glauert,' ... 'Karman-Tsien and Laitone compressibility rules']) disp([Mcr_PG Mcr_KT Mcr_L])...
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