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//Fluid Systems- By Shiv Kumar
//Chapter 5- Francis Turbine
//Example 5.11
//To Determine The Flow Rate, Guide Vane Angles, Runner Vane Angles and Inner and Outer Diameters of the Runner.
clc
clear
//Given Data:-
H=86.4; //Net Head, m
N=650; //Speed, rpm
P=397; //Shaft Power, kW
bo_by_Do=0.1; //Breadth Ratio
Di_by_Do=0.5; //Di/Do
Kf=0.17; //Flow Ratio
eta_H=95/100; //Hydraulic Efficiency
eta_o=85/100; //Overall Efficiency
//As Discharge is Radial and Flow Velocity is Constant,
alpha_o=90; //degrees //Vfi=Vfo=Vo
//Data Required:-
rho=1000; //Density of Water, Kg/m^3
g=9.81; //Acceleration due to gravity, m/s^2
//Computations:-
Q=P*1000/(rho*g*H*eta_o); //m^3/s
Vfi=Kf*sqrt(2*g*H); //m/s
Vfo=Vfi;
Do=sqrt(Q/(%pi*bo_by_Do*Vfi)); //m
Di=Do*Di_by_Do; //m
ui=%pi*Do*N/60; //m/s
uo= %pi*Di*N/60; //m/s
Vwi=eta_H*g*H/ui; //m/s
alpha_i=atand(Vfi/Vwi); //degrees
beta_i=atand(Vfi/(Vwi-ui)); //Runner Vane Angle at Inlet, degrees
beta_o=atand(Vfo/uo); //Runner Vane Angle at Outlet, degrees
//Results:-
printf(" (i) The Flow Rate, Q=%.3f m^3/s\n",Q )
printf(" (ii) Guide Vane Angles are: \n alpha_i=%.2f Degrees , alpha_o=%.f Degrees\n",alpha_i,alpha_o) //The Answer Vary due to Round off Error
printf(" (iii) Runner Vane Angles are:- \n beta_i=%.2f Degrees , beta_o =%.2f Degrees \n",beta_i,beta_o ) //The Answer Vary due to Round off Error
printf(" (iv) Inner and Outer Diameters of the Runner are: \n Di=%.2f m , Do=%.2f m \n",Di,Do )
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