Example 4.4-1 Laminar Flow along a Flat Plate (approximate Solution) > restart; > Ibook1:=mu*D[2](vx)(x,0); > Ibook2:=-rho*diff(int(vx(x,y)*(ve(x)-vx(x,y)),y=0...b(x)),x); > Ibook3:=-rho*D(ve)(x)*int(ve(x)-vx(x,y),y=0..b(x));
> Ibook:=Ibook1+Ibook2+Ibook3; Eq. 4.4-13 with terms expanded by Maple > vx:=(x,y)->vinf*(3/2*y/delta(x)-1/2*(y/delta(x))^3); assumed variation of vx in the boundary layer.
> ve:=x->vinf;b:=x->delta(x); for a flat plate with the integration carried out over the thickness delta(x) > Ibook1; > Ibook2; > Ibook3; > Ibook:=Ibook1+Ibook2; Eq. 4.4-16
> s:=dsolve({Ibook,delta(0)=0},delta(x));
> assign(s[2]);delta:=unapply(delta(x),x); choosing the positive root. > vx(x,y); Eq. 4.4-18
> tau0:=-mu*D[2](vx)(x,0);
> Fx:=-2*int(int(tau0,x=0...L),z=0...W); > evalf(Fx); Eq. 4.4-19