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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
+
+