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//Fluid Systems- By Shiv Kumar
//Chapter 7- Performance of Water Turbine
//Example 7.14
//To Determine the Size (Scale Ratio) of the Model and To Find the Model Speed and Power.
clc
clear
//Given:-
TP=240000; //Total Power Produced, kW
n=4; //No. of Turbines
eta_o=91/100; //Effeciency of each turbine
Np=120; //Speed of each Turbine, rpm
Hp=70; //Head for each Turbine, m
Qm=0.45; //Discharge for Model, m^3/s
Hm=5; //Head for testing the Model, m
//Data Required:-
rho=1000; //Density of Water, Kg/m^3
g=9.81; //Acceleratrion due to gravity, m/s^2
//Calculations:-
Pp=TP/n; //Power produced from each Turbine, kW
Qp=Pp*1000/(rho*g*Hp*eta_o); //Discharge passing through one Turbine, m^3/s
DmbyDp=(Qm/Qp)^(1/2)*(Hp/Hm)^(1/4); //From Relation of Flow Coefficient
Lr=DmbyDp; //Scale Ratio
Nm=(Np/DmbyDp)*(Hm/Hp)^(1/2); //rpm
Pm=Pp*(Nm/Np)^3*DmbyDp^5; //KW
//Results
printf("The Scale Ratio is 1:%.2f\n ",1/Lr)
printf("Model Speed, Nm=%.2f rpm\n",Nm)
printf("Model Power, Pm=%.2f kW\n",Pm) //The Answer vary due to Round off Error
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