Question

Someone claims that in fully developed turbulent flow in a tube, the shear stress is a maximum at the tube surface. Do you agree with this claim? Explain.

Short answer

Answer: In fully developed turbulent flow within a tube, the shear stress is maximum at the tube surface. This is because the velocity decreases when it approaches the surface, leading to a higher velocity gradient near the surface, which results in an increased shear stress.

Step-by-step solution

Understand Turbulent Flow

Turbulent flow is characterized by chaotic and disordered fluid movements, with complex eddies and vortices present. In fully developed turbulent flow within a tube, the velocity and pressure distribution follow specific patterns.

Shear Stress in Turbulent Flow

In fluid dynamics, shear stress is related to the velocity gradient perpendicular to the flow direction. The wall shear stress is the force exerted by the fluid on the inner surface of the tube, which is responsible for the skin friction drag. In laminar flow, the shear stress has a linear distribution, but in turbulent flow, the distribution is more complex, and this complexity increases as we move toward the wall.

Maximum Shear Stress at Tube Surface

In fully developed turbulent flow, the velocity decreases as we approach the surface, reaching zero at the wall due to the no-slip condition. As the velocity decreases, the gradient of velocity (rate of change of velocity with respect to distance from the wall) increases, resulting in higher shear stress near the surface. Thus, the shear stress is indeed maximum at the tube surface in fully developed turbulent flow.

Impact of Turbulence Near Wall

The presence of turbulent structures, such as turbulent boundary layers and eddies, can significantly alter the flow dynamics near the wall. These turbulent structures play an essential role in increasing the shear stress at the surface. The high shear stress near the wall increases the overall resistance to the fluid flow, contributing to the higher pressure drop observed in turbulent flow.

Conclusion and Agreement

Based on the above analysis, we can agree with the claim that the shear stress is maximum at the tube surface in fully developed turbulent flow. The chaotic fluid movements of turbulent flow lead to high velocity gradients near the tube surface, which, in turn, result in maximum shear stress.