Shear stress in laminar flow through a round pipe

Laminar flow is a type of fluid flow where the fluid moves in smooth layers or streams without any significant mixing between the layers. In the case of laminar flow through a round pipe, the shear stress can vary across the cross-section of the pipe.

Understanding shear stress

Shear stress is the force per unit area acting tangentially to a surface. In fluid flow, shear stress is caused by the frictional forces between adjacent layers of the fluid as they move relative to each other. In a round pipe, the shear stress is highest at the wall of the pipe and decreases as we move towards the center.

Shear stress distribution in a round pipe

In laminar flow through a round pipe, the shear stress distribution across the pipe cross-section can be approximated by a parabolic profile. This means that the shear stress is highest at the wall of the pipe, decreases linearly towards the center, and becomes zero at the centerline of the pipe.

The parabolic distribution of shear stress arises from the velocity profile of the fluid in laminar flow. In laminar flow, the velocity is highest at the centerline of the pipe and decreases linearly towards the wall. Since shear stress is directly proportional to velocity gradient, the shear stress distribution follows a parabolic pattern.

Explanation of the correct answer

The correct answer is option 'B' - the shear stress varies linearly with the radial distance. This means that as we move from the wall of the pipe towards the center, the shear stress decreases linearly.

This answer is consistent with the parabolic distribution of shear stress in laminar flow through a round pipe. The linear variation of shear stress with radial distance indicates that the shear stress is highest at the wall and decreases uniformly as we move towards the center of the pipe.

Conclusion

In summary, for laminar flow through a round pipe, the shear stress varies linearly with the radial distance. This variation arises from the parabolic velocity profile in laminar flow, where the velocity is highest at the centerline of the pipe and decreases linearly towards the wall. Understanding the shear stress distribution is important in analyzing fluid flow behavior and designing pipe systems.