Assignment:
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 given 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, showing the 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)