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//Fluid Systems- By Shiv Kumar
//Chapter 5- Francis Turbine
//Example 5.3
//To Find (a)The Absolute Velocity of Water at Inlet of Runner (b)The Velocity of Whirl at Inlet (c) The Relative Velocity at Inlet
//(d) The Runner Blade Angles (e)Width of Runner at Outlet (f)Weight of Water flowing through the Runner per second
//(g)Head at Inlet of the Turbine (h)Power developed (i) Hydraulic Efficiency of the Turbine
clc
clear
//Given Data:-
Do=1; // External Diameter of Runner, m
Di=0.5; //Internal Diameter of Runner, m
N=200; //Speed of Turbine, rpm
bo=225; //Width of Runner at Inlet, mm
Vfi=2.15; //Velocity of flow at Inlet, m/s
// As Velocity of Flow is constant through the Runner,
Vfo=Vfi; //Velocity of flow at Outlet, m/s
Vo=Vfo;
alpha_i=11; //Guide Blades Angle at Inlet, degrees
//As Discharge at Outlet of the Turbine is Radial,
alpha_o=90; //Guide Blades angle at Outlet, degrees
Vwo=0;
//Data Required:-
rho=1000; //Density of Water, Kg/m^3
g=9.81; //Acceleration due to gravity, m/s^2
//Computations:-
ui=%pi*Do*N/60; //m/s
// (a)The Absolute Velocity of Water at Inlet of Runner,
Vi=Vfi/sind(alpha_i); //m/s
//(b)The Velocity of Whirl at Inlet,
Vwi=Vfi/tand(alpha_i); //m/s
// (c) The Relative Velocity at Inlet,
Vri=sqrt(Vfi^2+(Vwi-ui)^2); //m/s
// (d) The Runner Blade Angles, beta_i, beta_o
beta_i=asind(Vfi/Vri); //Runner Blade Angle at Inlet, degrees
uo=%pi*Di*N/60; //m/s
beta_o=atand(Vfo/uo); //Runner Blade Angle at Outlet, degrees
// (e)Width of Runner at Outlet , bi
bi=Do*bo/Di; //mm
// (f)Weight of Water flowing through the Runner per second, W
W=rho*g*%pi*Do*(bo/1000)*Vfi/1000; //kN/s
//(g)Head at Inlet of the Turbine, H
H=Vwi*ui/g+Vo^2/(2*g); //m
// (h)Power developed by the Runner,
Q=%pi*Do*(bo/1000)*Vfi; //m^3/s
P=rho*Q*Vwi*ui/1000; //kW
//(i)Hydraulic Efficiency, eta_H
eta_H=Vwi*ui*100/(g*H); //In Percentage
//Results:-
printf("(a)The Absolute Velocity of Water at Inlet of Runner, Vi=%.3f m/s\n",Vi) //The Answer Vary due to Round off Error
printf(" (b)The Velocity of Whirl at Inlet, Vwi=%.2f m/s\n",Vwi)
printf(" (c) The Relative Velocity at Inlet, Vri=%.2f m/s\n",Vri)
printf(" (d) The Runner Blade Angles are:- \n beta_i =%.2f Degrees and beta_o =%.2f Degrees\n",beta_i,beta_o) //The Answer Vary due to Round off Error
printf(" (e)Width of Runner at Outlet , bi =%.f mm\n",bi)
printf(" (f)Weight of Water flowing through the Runner per second, W =%.2f kN/s\n",W) //The Answer Vary due to Round off Error
printf(" (g)Head at Inlet of the Turbine, H =%.3f m\n",H) //The Answer Vary due to Round off Error
printf(" (h)Power developed by the Runner =%.3f kW\n",P) //The Answer Vary due to Round off Error
printf(" (i)Hydraulic Efficiency, eta_H =%.2f Percent\n",eta_H) //The Answer Vary due to Round off Error
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