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+
+
+
+//exapple 11.3 
+clc; funcprot(0);
+// Initialization of Variable
+g=9.81;
+rhos=1980;//density of ore
+rho=1.218;//density of air
+e=0.4;
+mu=1.73/10^5;
+s=0;
+wp=[0 .08 .20 .40 .60 .80 .90 1.00];//weight percent
+d=[0.4 0.5 0.56 0.62 0.68 0.76 0.84 0.94]/1000;
+//part 1
+for i=1:7
+    dav(i)=d(i+1)/2+d(i)/2;//average dia
+    mf(i)=wp(i+1)-wp(i);//mass fraction
+    a(i)=mf(i)/dav(i);
+    s=s+a(i);
+end
+db=1/s;//d bar
+//quadratic coeff. ax^2 +bx +c=0
+c=-(rhos-rho)*g;
+b=150*(1-e)/e^3/db^2*mu;
+a=1.75*rho/e^3/db;
+y=poly([c b a],'U','coeff');
+U=roots(y);
+disp(abs(U(2)), "the linear air flow rate in (m/s):");
+//part 2
+d=0.4/1000;
+a=2*d^3/3/mu^2*rho*(rhos-rho)*g;
+a=log10(a);
+disp(a,"log10(Re^2/rho/U^2*R)=");
+//using chart
+Re=10^1.853;
+u=Re*mu/rho/d;
+disp(u, "speed required for smallest particle in (m/s):")