Calculation of the pressure field

Now we can calculate the pressure field.  This could be from the Bernoulli equation or from the r component of the N-S equation.  Lets use the latter.  

dpdr = -(vrpsi*D[vrpsi, r] + (vthpsi*D[vrpsi, θ])/r - 
        vthpsi^2/r)

dpdrtemp = Simplify[dpdr /. 
    {Derivative[a1_, a2_][ψ][r, θ] :> 
      D[psianswer, {r, a1}, {θ, a2}], 
     ψ[r, th] -> psianswer}]

If we form the definite integral for pressure as a function of r, we would have p(r->∞) - p(r) =

It is clear that these die off in distance.  Let's make the far away pressure = 0, i.e., rwayway ==> really far away.  If this is the case, then the second and 4th terms are 0.   The pressure as a function of r and theta is:

It is interesting to see what the pressure on the surface of the sphere is.

psurface=Simplify[pofr/.r->R]

Now what is the maximum pressure?

pstag=psurface/.θ->0