Discussion
The figure shows the developing zone and the fully developed region in a pipe flow where the steady flow takes place from left to right. The wall shear stress in the sections A, B, C, and D are given by \(\tau_{A}, \tau_{B}, \tau_{C}\), and \(\tau_{D}\), respectively. Select the correct statement.
Answer: A
The correct statement is \(\tau_{A} \gt \tau_{B}\).
At the pipe entrance the boundary layer is very thin, so the velocity gradient at the wall, and with it the wall shear stress \(\tau = \mu (du/dy)_{wall}\), is large. As the boundary layer thickens along the developing zone the wall gradient falls, so the shear stress decreases with distance: section A, upstream of B, has the larger value.
Once the flow is fully developed the velocity profile no longer changes along the pipe, so the wall shear stress is constant: \(\tau_{C} = \tau_{D}\), which rules out \(\tau_{C} \gt \tau_{D}\). The fully developed value is the lowest along the pipe, so \(\tau_{C} \gt \tau_{B}\) is also wrong, as is \(\tau_{B} \gt \tau_{A}\).
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