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+//Example 14-12

+clc;clear;

+// Properties

+rho_w=998;// kg/m^3

+//Given values

+r_2=2.50;// m

+r_1=1.77;// m

+b_2=0.914; // m

+b_1=2.62; // m

+n=120; // rpm

+omega=12.57;// rad/s

+alpha_2=33;// degree

+v=599;// m^3/s

+g=9.81;// m/s^2

+

+//Calculation

+//(a)

+V_2n=(v/(2*%pi*r_2*b_2));//The normal component of velocity at the inlet in m/s

+V_2t=V_2n*tand(alpha_2);//The tangential velocity component at the inlet in m/s

+beta_2=atand(V_2n/((omega*r_2)-(V_2t)));

+disp('(a) alpha=10 degree')

+printf('The runner leading edge angle at runner inlet, beta_2=%0.1f degree\n',beta_2);

+//Equations 1 through 3 are repeated for the runner outlet, with the following results:

+V_1n=(v/(2*%pi*r_1*b_1));//

+alpha_1=10;// degree

+V_1t=V_1n*tand(alpha_1);

+beta_1=atand(V_1n/((omega*r_1)-(V_1t)));

+printf(' The runner blade trailing edge angle , beta_1=%0.1f degree\n',beta_1);

+W_shaft=(rho_w*omega*v*((r_2*V_2t)-((r_1*V_1t))))/10^6;

+W_shaft_hp=(W_shaft)*1341.02209;

+printf(' The shaft output power,W_shaft =%0.2e hp\n',W_shaft_hp);

+// Assume Efficiency of turbine=100%

+// bhp=W_shaft

+H_1=(W_shaft)*10^6/(rho_w*g*v);// m

+printf(' The required net head,H =%0.1f m\n',H_1);

+

+//

+disp('(b) alpha=0 degree')

+alpha_11=0;// degree

+V_11t=V_1n*tand(alpha_11);

+beta_11=atand(V_1n/((omega*r_1)-(V_11t)));// degree

+printf(' The runner blade trailing edge angle , beta_1=%0.1f degree\n',beta_11);

+W_shaft1=(rho_w*omega*v*((r_2*V_2t)-((r_1*V_11t))))/10^6;// MW

+W_shaft1_hp=(W_shaft1)*1341.02209;// hp

+printf(' The shaft output power,W_shaft =%0.2e hp\n',W_shaft1_hp);

+H_2=(W_shaft1)*10^6/(rho_w*g*v);// m

+printf(' The required net head,H =%0.1f m\n',H_2);

+

+//

+disp('(c) alpha=-10 degree')

+alpha_12=-10;// degree

+V_12t=V_1n*tand(alpha_12);

+beta_12=atand(V_1n/((omega*r_1)-(V_12t)));

+printf(' The runner blade trailing edge angle , beta_1=%0.1f degree\n',beta_12);

+W_shaft12=(rho_w*omega*v*((r_2*V_2t)-((r_1*V_12t))))/10^6;// MW

+W_shaft12_hp=(W_shaft12)*1341.02209;// hp

+printf(' The shaft output power,W_shaft =%0.2e hp\n',W_shaft12_hp);

+H_3=(W_shaft12)*10^6/(rho_w*g*v);// m

+printf(' The required net head,H =%0.1f m\n',H_3);

+alpha=[33 0 -10];

+bhp=[W_shaft W_shaft1 W_shaft12];

+H=[H_1 H_2 H_3];

+plot(alpha,H,'r');

+legend('H');

+xlabel('alpha,degrees');

+ylabel('H,m');

+set(gca(),"data_bounds",matrix([-30,30,0,100],2,-1));

+a = gca(); 

+a.y_location = "left"; 

+a.filled = "on"; 

+a.axes_visible = ["on","on","on"]; 

+a.font_size = 1; 

+b = newaxes(); 

+b.y_location = "right"; 

+b.filled = "off"; 

+b.axes_visible = ["off","on","on"]; 

+b.axes_bounds = a.axes_bounds; 

+b.y_label.text = "bhp,MW"; 

+b.font_size = a.font_size

+plot(alpha,bhp,'g');

+legend(['bhp'],"in_upper_left");

+set(gca(),"data_bounds",matrix([-30,30,0,700],2,-1));