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+clc;
+clear all;
+disp("i) displacement thickness to boundary thickness ratio")
+disp("velocity distribution: u/U=3y/(2*d)-y^2/(2*d^2)")
+disp("d* = integrate (1-3y/(2*d)-y^2/(2*d^2),y,0,d)")
+disp("d*/d = 5/12")
+disp("displacement thickness to bloundary thickness ratio : d*/d =5/12")
+disp("ii) momentum thickness to boundary layer thickness ratio")
+disp("th = integrate(u/U*(1-u/U),y,0,d)")
+disp("th = integrate(((1-3y/(2*d)-y^2/(2*d^2))*(1-((1-3y/(2*d)-y^2/(2*d^2))),y,0,d)")
+disp("thus, th/d = 19/120")
+disp(" momentum thickness to boundary layer thickness ratio = 19/120")
+