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Representative velocity profiles

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:

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)

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Solution Preview

Hi, your problem has a solution that can be very simple. This solution is call the Blasius 1/7 power law (see page 170 - 171 of Bennet - Myers, Momentum, Heat and Mass Transfer, edition TMH of Tata Mc Graw Hill Publishing Company).

That law is u/umax ...

Solution Summary

This solution explains in 170 words how the Blasius 1/7 power law can be used to find the velocity of flow in a system. Calculations for boundary thickness are also provided to explain how delta can be computed for each length of conduction.