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+// Display mode

+mode(0);

+// Display warning for floating point exception

+ieee(1);

+clear;

+clc;

+disp("Turbomachinery Design and Theory,Rama S. R. Gorla and Aijaz A. Khan, Chapter 5, Example 15")

+disp("Angles are in degrees, lengths in meters, velocities in m/s, temperatures are in Kelvins")

+disp("Using Equation at the mean radius")

+disp("Wc = Cp(DeltaTA + DeltaTB) =DeltaTS")

+disp("Dif = T02-T01") 

+Dif = 20;

+tau = 0.94;

+U = 200;

+Ca = 155;

+Cp = 1005;

+N = 8000;

+disp("tan(beta1)-tan(beta2) = Dift ------(A)")

+Dift = Dif*Cp/(tau*U*Ca)

+disp("Using Equation, the degree of reaction (DOF) is")

+disp("DOF = Ca*(tan(beta1)+tan(beta2))/(2U)")

+disp("tan(beta1)+tan(beta2) = Add ------(B)")

+DOF = 0.5;

+Add = DOF*2*U/Ca

+disp("Solving (A) and (B) equations simultaneously")

+beta1 = atan((Add+Dift)/2)*180/%pi

+alpha2 = beta1;

+beta2 = atan(1.29-tan(beta1*%pi/180))*180/%pi

+alpha1 = beta2;

+disp("Let rm be the mean radius")

+rm = U/(2*%pi*N)//m

+disp("Using continuity equation in order to find the annulus area of flow")

+C1 = Ca/cos(alpha1*%pi/180)//m/s

+T01 = 290;

+T1 = T01-C1^2 /(2*Cp)

+disp("Using isentropic relationship at inlet: p1/p01 = (T1/T01)^(gamma/(gamma-1))")

+disp("Static pressure is P1 in bars")

+P01 = 1;

+P1 = P01*(T1/T01)^3.5

+disp("Density in kg/m3")

+R = 287;

+rho1 = P1/(R*T1) *10^5

+disp("From the continuity equation,")

+m = 22;//kg

+A = m/(rho1*Ca)

+disp("blade height in m is")

+h = A/(2*%pi*rm)

+disp("At mean radius, and noting that blades beta, an equivalent to cascade, alpha, nominal air deflection is Epsilon")

+Epsilon = beta1-beta2

+disp("Using Fig. Ex515 for cascade nominal deflection vs. air outlet angle, the solidity,")

+disp("s/c = 0.5")

+disp("Blade aspect ratio = span/chord")

+disp("Blade chord = C")

+C = 0.089/3

+disp("Blade pitch = s")

+s = 0.5*C

+disp("Both the Chord and pitch/span are in meters")