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
> vx:=(x,y)->vinf*(3/2*y/delta(x)-1/2*(y/delta(x))^3);
![[Maple Math]](images/ex441c1.gif)
> ve:=x->vinf;
> Ibook1;
> Ibook2;
> Ibook3;
> Ibook:=Ibook1+Ibook2;
> b:=x->delta(x);
> b(x);
> Ibook; Eq. 4.4-16
![[Maple Math]](images/ex441c2.gif)
> s:=dsolve({Ibook,delta(0)=0},delta(x));
> assign(s[1]);delta:=unapply(delta(x),x);
![[Maple Math]](images/ex441c3.gif)
> vx(x,y); Eq. 4.4-18
![[Maple Math]](images/ex441c4.gif)
> tau0:=-mu*D[2](vx)(x,0);
> Fx:=-2*int(int(tau0,x=0...L),z=0...W);
> evalf(Fx); Eq. 4.4-19
![[Maple Math]](images/ex441c5.gif)
>