Answer:

The Average Shear Stress in the Bed of the Canal

The average shear stress in the bed of a canal refers to the force per unit area acting parallel to the bed, which is responsible for the movement or resistance of the fluid flow. In the context of fluid mechanics, this shear stress is closely related to the tractive force per unit area.

Shear Stress and Tractive Force

Shear stress is defined as the force per unit area required to cause the flow of a fluid parallel to the bed or within a fluid medium. It is often represented by the Greek letter tau (τ). Tractive force, on the other hand, refers to the force exerted by a fluid on a solid surface, such as the bed of a canal.

The Relationship between Shear Stress and Tractive Force

The average shear stress in the bed of a canal is equal to the tractive force per unit area. This relationship can be understood by considering the forces acting on a fluid element within the canal. The tractive force acting on the fluid element is exerted by the bed of the canal in the form of shear stress.

When the fluid is in motion, the shear stress at the bed of the canal is responsible for the fluid's ability to overcome the resistance offered by the bed and continue flowing. The tractive force per unit area represents the force exerted by the fluid on the bed, which is equal to the shear stress.

Implications and Applications

Understanding the relationship between shear stress and tractive force is crucial in the design and analysis of canals and other fluid flow systems. By considering the average shear stress in the bed of a canal, engineers can determine the tractive force required to maintain a desired flow rate and prevent sedimentation or blockages.

This relationship also has implications for sediment transport in canals. If the tractive force per unit area is insufficient to overcome the shear stress exerted by the bed, sediment particles may settle and accumulate, leading to reduced flow capacity and increased maintenance requirements.

In conclusion, the statement that the average shear stress in the bed of a canal is equal to the tractive force per unit area is true. This relationship is fundamental in fluid mechanics and has important implications for the design and operation of canals.