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+// scilab Code Exa 18.43 Francis turbine 250 rpm

+

+NS=0.4; //specific speed

+N=250; // Speed in RPM

+H=75; // net head in m

+beta3=25; // exit angle of the runner blades

+n_o=0.81; // overall efficiency

+g=9.81; // gravitational acceleration in m/s2

+rho=1000; // density in kg/m3

+// part(a)

+u2=0.6*sqrt(2*g*H);

+cr2=0.21*sqrt(2*g*H);

+omega=%pi*2*N/60;

+Q=(NS^2)*(H^(3/2))/((0.1804^2)*(omega^2));

+disp("m3/s",Q,"(a)the discharge rate for the turbine is")

+// part(b)

+d2=u2*60/(%pi*N);

+disp("m",d2,"(b)outer diameter of the runner blade ring is")

+cr3=cr2;

+cx3=cr3;

+//Euler work,w_ET=u2*c_theta2

+c_theta2=((g*H)-(0.5*(cx3^2)))/u2;

+u3=cx3/(tand(beta3));

+d3=u3*60/(%pi*N);

+disp("m",d3,"and inner diameter of the runner blade ring is")

+// part(c)

+alpha2=atand(cr2/c_theta2);

+disp("degree",alpha2,"(c)the inlet guide vane exit angle is")

+beta2=atand(cr2/(c_theta2-u2));

+disp("degree",beta2,"and inlet angle of the runner blades is beta2= ")

+// part(d)

+n_h=(u2*c_theta2)/(g*H);

+disp("%",n_h*1e2,"(d)the hydraulic efficiency is")

+// part(e)

+P=n_o*rho*g*Q*H;

+disp("MW",P*1e-6,"(e)the output power is")

+disp("comment: the calculation for c_theta2 is done wrongly in the book. hence the values of alpha2,beta2, n_h differs from the book.")