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+
+
+//example 12.1 
+clc; funcprot(0);
+// Initialization of Variable
+rho=1.22;
+pi=3.1428;
+rhos=518;
+rhoav=321;
+mu=1.73/10^5;
+g=9.81;
+d=0.65/1000;
+d2=25.5/100;//dia of duct
+ms=22.7/60;//mass flow rate
+//calculation
+e=(rhos-rhoav)/(rhos-rho);
+//coeff of quadratic eqn in U
+//a*x^2+b*x+c=0
+c=-(1-e)*(rhos-rho)*g;
+b=150*(1-e)^2*mu/d^2/e^3;
+a=1.75*(1-e)*rho/d/e^3;
+y=poly([c b a],'U','coeff');
+U=roots(y);
+Us=ms*4/pi/d2^2/rhos;//superficial speed
+Ua=e/e*(U(2)/e+Us/(1-e));
+disp(Ua,"the actual linear flow rate through duct in (m/s):")