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+// scilab Code Exa 18.44 Pelton Wheel 360 rpm

+

+d=2; // mean diameter in m

+N=360; // Speed in RPM

+theta=150; //deflection angle of water jet in degree

+H=140; // net head for the model in m

+q=45000; // discharge in litres/min

+Q=q*1e-3/60; // in m3/s

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

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

+// part(a)

+u=%pi*d*N/60;

+c2=sqrt(2*g*H);

+sigma=u/c2;

+disp(sigma,"(a)blade to jet speed ratio is")

+// part(b)

+w2=c2-u;

+w3=w2;

+beta2=0;

+beta3=180-theta;

+cy2=c2;

+cy3=u-(w3*cosd(beta3));

+w_T=u*(cy2-cy3);

+m=rho*Q;

+P_T=m*w_T;

+disp("kW",P_T*1e-3,"(b)the power developed is")

+// part(c)

+n=w_T/(0.5*(c2^2));

+disp("%",n*1e2,"(c)the efficiency is")

+// part(d)

+n_max=0.5*(1+cosd(beta3));

+disp("%",n_max*1e2,"(d)the Maximum efficiency is")

+P_max=m*g*H*n_max;

+disp("kW",P_max*1e-3,"and the Maximum power developed is")

+// part(e)

+sigma_opt=0.5; // for Maximum efficiency

+u_opt=sigma_opt*c2;

+N_opt=u_opt*60/(d*%pi);

+disp("rpm",N_opt,"(e)speed of the rotation corresponding to Maximum efficiency is")

+// part(f)

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

+NS=omega*sqrt(P_T)*(H^(-5/4))/549.016;

+disp(NS,"(f)the specific speed of turbine is")