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.
In pipe flow, the wall shear stress is related to the velocity gradient at the pipe wall. The velocity profile in the developing zone is still changing, meaning that the fluid velocity near the wall is higher compared to the fully developed region. As a result, the velocity gradient at the wall is higher in the developing zone, leading to a higher wall shear stress.
Step 1: Wall Shear Stress in the Developing Zone
In the developing zone (section A), the flow has not yet reached the steady state, so the velocity profile is still developing. The velocity gradient near the wall is large, resulting in a higher shear stress at the wall.
Step 2: Wall Shear Stress in the Fully Developed Region
In the fully developed region (sections B, C, and D), the velocity profile becomes stable and does not change with distance along the pipe. The wall shear stress becomes constant. The shear stress in section B, which is in the fully developed region, is lower than in section A because the flow is no longer changing.
Step 3: Conclusion
Thus, \( \tau_A > \tau_B \) because the wall shear stress in the developing zone is higher due to the larger velocity gradient. Therefore, the correct answer is (A).
