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//Fluid Systems- By Shiv Kumar
//Chapter 5- Francis Turbine
//Example 5.12
clc
clear
//Given Data:-
Dp=5; //Diameter at Penstock, m
P=61000; //Output Power, kW
Q=110; //Discharge, m^3/s
N=160; //Speed, rpm
eta_H=94/100; //Hydraulic Efficiency
Do=4; //Diameter of Runner at Inlet, m
bo=1; //Width of Runner at Inlet, m
Ddi=4.2; //Entry Diameter to Draft Tube, m
V2=2.2; //Velocity in Tail Race, m/s
p_by_rho_g=58; //Static Pressure Head (p/(rho*g)) , m
Z=2.8; //Level of Measurement above Tail Race, m
loss=25; //Percentage of loss in Draft Tube (of Velocity Head at its Entry)
Z1=2.2; //Level of Runner Exit above Tail Race, m
//Data Required:-
rho=1000; //Density of Water, Kg/m^3
g=9.81; //Acceleration due to gravity, m/s^2
//Computations:-
Vp=4*Q/(%pi*Dp^2); //Velocity in Penstock, m/s
Vo=4*Q/(%pi*Ddi^2); //Velocity at Entry to the Draft Tube, m/s
Hp=p_by_rho_g+Z+Vp^2/(2*g); //Head just before Entry to Runner, m
H=Hp-V2^2/(2*g); //Working Head, m
//(a)Overall Efficiency
eta_o=P*1000/(rho*Q*g*H)*100; //In Percentage
// (b) The Direction of Flow relative to the Runner at Inlet
ui=%pi*Do*N/60; //m/s
Vwi=eta_H*g*H/ui; //m/s
Vfi=Q/(%pi*Do*bo); //m/s
beta_i=180-atand(Vfi/(ui-Vwi)); //degrees
// (c) The Pressure Head at entry to Draft Tube, p1/(rho*g)
//By Applying Bernoulli's Equation with,
Z2=0;
p2_by_rho_g=0;
hf=(loss/100)*Vo^2/(2*g);
p1_by_rho_g=p2_by_rho_g+(V2^2-Vo^2)/(2*g)+(Z2-Z1)+hf; //m
//Results:-
printf("(a)The Overall Efficiency, eta_o=%.2f Percent\n",eta_o) //The Answer Vary due to Round off Error
printf("(b)The Direction of Flow relative to the Runner at Inlet, beta_i=%.2f Degrees \n",beta_i) //The Answer Vary due to Round off Error
printf("(c) The Pressure Head at entry to Draft Tube, p1/(rho*g)=%.2f m (vaccum)\n",abs(p1_by_rho_g))
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