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//Fluid system - By - Shiv Kumar
//Chapter 4 - Pelton Turbine (Impulse Turbine)
//Example 4.8
clc
clear
//Given Data:-
Cv=0.97; //Co-efficient of Velocity
H_l=400; //Head at lake, m
d=80; //Diameter of Jet, mm
D_pipe=0.6; //Diameter of pipe, m
l=4; //Length of pipe, m
f_dash=0.032; //Friction factor
AoD=165; //Angle of Deflection, degrees
beta_o=180-AoD; //degrees
// As bucket runs at 0.48 Jet speed
u_by_Vi=0.48; //u/Vi
Vel_per=15; //percentage by which velocity is reduced
eta_m=90/100; //Mechanical Efficiency
//Data Used:-
rho=1000; //Density of water, kg/m^3
g=9.81; //Acceleration due to gravity, m/s^2
//Computations:-
d=d/1000; //m
l=l*1000; //m
Vro_by_Vri=1-Vel_per/100; //Vro/Vri
//using continuity equation,
V_by_Vi=(d/D_pipe)^2; //V/Vi
Vi=sqrt((2*g*H_l)/(1/Cv^2+f_dash*l*V_by_Vi^2/D_pipe)); //m/s
Vwi=Vi;
u=Vi*u_by_Vi; //m/s
ui=u;
uo=u;
Vri=Vi-ui; //m/s
Vro=Vri*Vro_by_Vri; //m/s
Vrwo=Vro*cosd(beta_o); //m/s
//(i) Flow Rate, Q
Q=(%pi/4)*d^2*Vi; //m^3/s
//(ii) Shaft Power, P
Vwo=uo-Vrwo; //m/s
Pr=rho*Q*(Vwi-Vwo)*u/1000; //Power developed by the runner, kW
P=eta_m*Pr; //kW
//Results:-
printf("Flow Rate, Q=%.4f m^3/s \n", Q) //The answer vary due to round off error
printf("Shaft power, P=%.2f kW", P) //The answer vary due to round off error
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