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//Fluid Systems- By Shiv Kumar
//Chapter 5- Francis Turbine
//Example 5.4
//To Find (a)Diameter and Width at Inlet ant Outlet (b)Runner Vane Angles at Inlet and Outlet (c)Guide Blade Angles
clc
clear
//Given Data:-
H=70; //Net Head, m
N=700; //Speed, rpm
P=330; //Shaft Power, kW
eta_o=85/100; //Overall Efficiency
eta_H=92/100; //Hydraulic Efficiency
Kf=0.22; //Flow Ratio
bo_by_Do=0.1; //Breadth Ratio
t_per=6; //Percentage of Circumferential Area occupied by the Thickness of Vanes
Kt=1-t_per/100; //Vane Thickness Factor
//As Outer Diameter= 2 times the Inner Diameter,
Do_by_Di=2; //Do/Di
//Data Required:-
rho=1000; //Density of Water, Kg/m^3
g=9.81; //Acceleration due to gravity, m/s^2
//Computations:-
Vfi=Kf*sqrt(2*g*H); //m/s
Vfo=Vfi;
Q=P*1000/(rho*g*H*eta_o); //m^3/s
//(a)Diameter and Width at Inlet ant Outlet, Do,bo, Di and bi.
Do=sqrt(Q/(Kt*%pi*bo_by_Do*Vfi)); //m
Di=Do/Do_by_Di; //m
bo=Do*bo_by_Do*1000; //mm
bi=Do*bo/Di; //mm
ui=%pi*Do*N/60; //m/s
uo=%pi*Di*N/60; //m/s
Vwi=eta_H*g*H/ui; //m/s
// (b)Runner Vane Angles at Inlet and Outlet, beta_i,beta_o
beta_i=atand(Vfi/(Vwi-ui)); //Runner Vane Angle at Inlet, degrees
beta_o=atand(Vfo/uo); //Runner Vane Angle at Outlet, degrees
//(c)Guide Vane Angle, alpha_i
alpha_i=atand(Vfi/Vwi); //degrees
//As flow is radial at outlet,
alpha_o=90; //degrees
//Results:-
printf(" (a)Diameter and Width at Inlet and Outlet are: \n\t")
printf("Do=%.3f m bo=%.1f mm\n Di=%.3f m bi=%.1f mm\n",Do,bo,Di,bi) //The Answer Vary due to Round off Error
printf(" (b)Runner Vane Angles at Inlet and Outlet are:- \n beta_i=%.2f Degrees , beta_o =%.2f Degrees \n",beta_i,beta_o) //The Answer Vary due to Round off Error
printf(" (c)Guide Vane Angles, \n alpha_i=%.2f Degrees , alpha_o=%.f Degrees\n ",alpha_i,alpha_o) //The Answer Vary due to Round off Error
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