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diff --git a/51/DEPENDENCIES/8_4.sce b/51/DEPENDENCIES/8_4.sce
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+clc;
+clear;
+exec("C:\Program Files\scilab-5.3.0\bin\TCP\8_4data.sci");
+stress=D*(pgrad*1000)/(4*1);//N/(m^2)
+uf=(stress/d)^0.5;//m/sec; where uf is frictional velocity
+ts=5*kvis*1000/(uf);//mm; where ts is the thickness of the viscous sublayer
+disp("mm",ts,"The thickness of the viscous sublayer=")
+V=Q/(%pi*(D^2)/4);//m/s
+Re=V*D/kvis;
+disp("hence the flow is turbulent.",Re,"The reynolds number=")
+n=8.4;//from turbulent flow velocity profile diagram
+
+//Q=(%pi)*(R^2)*V
+R=1;//assumption
+//let Q/Vc=x
+x=integrate('((1-(r/R))^(1/n))*(2*%pi*r)','r',0,R);
+q=%pi*(R^2)*V;
+Vc=q/x;//m/s
+disp("m/s",Vc,"The approximate centerline velocity=")
+stress1=(2*stress*r)/D;//N/(m^2)
+//d(uavg)/dr=urate=-(Vc/(n*R))*((1-(r/R))^((1-n)/n)); where uavg=average velocity
+urate=-(Vc/(n*(D/2)))*((1-(r/(D/2)))^((1-n)/n));//s^(-1)
+stresslam=-(kvis*d*urate);//N/(m^2)
+stressratio=(stress1-stresslam)/stresslam;
+disp(stressratio,"The ratio of teh turbulent to laminar stress at a point midway between the centreline and the pipe wall =")
+\ No newline at end of file