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//Fluid Systems- By Shiv Kumar
//Chapter 5- Francis Turbine
//Example 5.7
//To Determine (a) The Diameter of Wheel (b) The Quantity of Water Supplied (c) The Guide Blade Angle at Inlet (d) The Runner Vane Angles at Inlet and Exit.
clc
clear
//Given Data:-
P=368; //Shaft Power, kW
H=71; //Head, m
N=748; //Speed, rpm
bo_by_Do=0.1; //Breadth Ratio
Kf=0.15; //Flow Ratio
eta_H=95/100; //Hydraulic Efficiency
eta_m=85/100; //Mechanical Efficiency
eta_v=100/100; //Volumetric Efficiency (Assumed to be 100%)
//As Inner Diameter is Half the Outer Diameter,
Di_by_Do=1/2; //Di/Do
//Data Required:-
rho=1000; //Density of Water, Kg/m^3
g=9.81; //Acceleration due to gravity, m/s^2
//Computations:-
eta_o=eta_H*eta_m*eta_v; //Overall Efficiency
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
// (a) The Diameter of Wheel, Do
//Calculated Above
// (b) The Quantity of Water Supplied, Q
//Calculated Above
// (c) The Guide Blade Angle at Inlet , alpha_i
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
// (d)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
//Results:-
printf(" (a) The Diameter of Wheel, Do =%.3f m\n ",Do )
printf(" (b) The Quantity of Water Supplied, Q=%.4f m^3/s\n",Q )
printf(" (c) The Guide Blade Angle at Inlet , alpha_i=%.2f Degrees\n",alpha_i ) //The Answer Vary due to Round off Error
printf(" (d)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
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