Question

Consider turbulent flow in a pipe under isothermal conditions. Let r denote the radial coordinate and z denote the axial flow direction. On moving away from the wall towards the center of the pipe, the rz-component of the Reynolds stress

• A. Increases and then decreases
• B. Decreases and then increases
• C. Remains unchanged
• D. Only increases

Hint:

In turbulent pipe flow, the Reynolds stress typically increases near the pipe wall due to high shear, and decreases as we move toward the pipe center due to lower velocity gradients.

Answer 1

The Correct Option is A

The Reynolds stress in turbulent flow represents the exchange of momentum between different layers of fluid.

Step 1: Understand the behavior of Reynolds stress.
In a turbulent flow, the Reynolds stress component \( \tau_{rz} \) changes as we move from the wall towards the center of the pipe. Initially, near the pipe wall, the shear stress is large. As we move towards the center of the pipe, the turbulent intensity decreases, and the Reynolds stress starts to decrease as well.

Step 2: Conclusion.
The Reynolds stress initially increases near the wall, reaches a peak, and then decreases towards the center of the pipe. Hence, the correct answer is (A).

Final Answer: (A) Increases and then decreases