Discussion
In the case of a fully developed flow through a pipe, the shear stress at the centerline is
Answer: C
The shear stress at the centerline is zero.
In fully developed pipe flow the shear stress varies linearly with radius, from zero at the axis to its maximum at the wall:
\[ \tau(r) = \frac{r}{2}\left(-\frac{dp}{dx}\right) \]
This follows from a force balance on a cylinder of fluid of radius r, and holds for laminar and turbulent flow alike. At r = 0 the velocity profile has its maximum, so its slope, and hence the shear stress, is zero by symmetry.
It does not vary with axial distance, since the flow is fully developed; it does not depend on centerline velocity; and it is certainly not infinite.
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