Plot some representative velocity profiles for a purely oscillatory flow of a newtonian fluid in a long, rigid, straight pipe at various phases of the flow

Womersly’s Problem:

Plot some representative velocity profiles for the purely oscillatory
flow of a Newtonian fluid in a long, rigid, straight pipe at various
phases of the flow (3-4)

For these plots, use the values of constants give below:

Constants:

Velocity (u): 105 cm/s

Diamter (d): 2.23 cm

Kinematic viscosity (nu): 0.035 cm^2/s

Reynolds Number: 6690

Generate data for the plots simply by evaluating the solution at many
radii, must show evaluation of algebra. Note any characteristic shapes,
how do they change as alpha changes?

(For analytic solution of this problem, see the book by Schlichting and
see also Gerrard, J. Fluid Mech., 1971, 46)