Section 4.4 Flow near Solid Surfaces by Boundary Layer Theory
>  restart;
>  econ:=D[1](vx)(x,y)+D[2](vy)(x,y)=0;
>  emotx:=(x,y)->vx(x,y)*D[1](vx)(x,y)+vy(x,y)*D[2](vx)(x,y)+D(P)(x)/rho-nu*D[2](D[2](vx))(x,y); x component of eq. of motion (4.4-2) neglecting the second derivative of vx wrt x. This agrees with eq. 4.4-10.
>  vy:=(x,y)->-int(D[1](vx)(x,y1),y1=0...y); This should be a solution to the continuity equation.
>  econ; It is!

>  BE:=P(x)+rho*ve(x)^2/2; Bernoulli Equation: 4.3-5 for potential flow and neglecting vy in the potential flow region.
>  P(x):=solve(BE,P(x));P:=unapply(P(x),x);
>  emotx(x,y); This gives 4.4-12.

>  Ins:=array(1...4);
>  for k from 1 to 4 do
>   Ins[k]:=int(op(k,emotx(x,y)),y=0...b);
>  od;
>  Ins2:=-int(U(x,y)*D[2](vx)(x,y),y=0...b);
>  U:=(x,y)->int(D[1](vx)(x,y1),y1=0...y);
>  simplify(Ins2-Ins[2]);

>  Ins2:=-U(x,b)*ve(x)+int(vx(x,y)*D[2](U)(x,y),y=0...b); Using
a) int(UdV,0..b)=U(b)*V(b)-int(VdU),0...b) with V=vx(x,y)
b) dV=vx(x,y)dy
c) vx(x,0)=0, vx(x,b)=ve(x)

>  nu:=mu/rho;Itot:=simplify(rho*(Ins[1]+Ins2+Ins[3]+Ins[4]));
>  Ibook1:=mu*D[2](vx)(x,0);
>  Ibook2:=-rho*diff(int(vx(x,y)*(ve(x)-vx(x,y)),y=0...b),x);
>  Ibook3:=-rho*D(ve)(x)*int(ve(x)-vx(x,y),y=0..b);
>  dif:=simplify(expand(Itot-Ibook1-Ibook2-Ibook3));
>  op(1,dif);op(2,dif);op(3,dif);op(4,dif);op(5,dif);op(6,dif);
>  op(1,dif)+op(2,dif)+op(5,dif); These should cancel except for the last term: rho*int(vx(x,y)*D(ve)(x),y=0...b)=rho*D(ve)(x)*int(vx(x,y),y=0...b)


>  rho*D(ve)(x)*int(vx(x,y),y=0...b)+op(6,dif); These two then leave b*rho*D(ve)(x)*ve(x)

>  b*rho*D(ve)(x)*ve(x)+op(3,dif); Leaving only: op(4,dif)

>  op(4,dif); If b is large enough this should also vanish.