Boundary Layer Formation:

The boundary layer is a thin layer of fluid that forms on the surface of a solid object when it is in contact with a flowing fluid, such as air or water. This layer plays a crucial role in fluid dynamics and affects the behavior of the flow around the solid surface.

Explanation:

The correct answer to the question is option 'D' - the viscosity of the fluid. Viscosity is a measure of a fluid's resistance to flow and is a crucial factor in boundary layer formation. Let's delve into the details of how viscosity influences the formation of the boundary layer:

1. Introduction to Viscosity:
Viscosity is the internal friction within a fluid that resists its flow. It arises due to the cohesive forces between the fluid molecules. Viscosity determines the fluid's ability to flow smoothly and influences the rate at which the fluid layers slide over each other.

2. Role of Viscosity in Boundary Layer Formation:
When a fluid flows over a solid surface, the fluid molecules in direct contact with the surface experience the no-slip condition. This means that the fluid velocity at the surface is zero. As a result, the fluid molecules in contact with the surface come to a relative standstill.

The fluid layers above these stationary molecules continue to flow, leading to a velocity gradient from zero at the surface to the free-stream velocity of the fluid. This velocity gradient is responsible for the development of the boundary layer.

Viscosity plays a crucial role in this process. The fluid molecules in contact with the solid surface transfer their momentum to the adjacent layers through molecular interactions. This momentum transfer creates a shearing effect between the fluid layers, and viscosity determines the magnitude of this shearing.

3. Boundary Layer Characteristics:
The boundary layer is characterized by two distinct regions - the laminar boundary layer and the turbulent boundary layer. The type of boundary layer that forms depends on the fluid's viscosity and the flow conditions.

- Laminar Boundary Layer: In a laminar boundary layer, the fluid flows smoothly in parallel layers with minimal mixing. This type of boundary layer is more likely to form at lower flow velocities and lower viscosity fluids.
- Turbulent Boundary Layer: In a turbulent boundary layer, the fluid flow becomes chaotic and highly mixed. This type of boundary layer is more likely to form at higher flow velocities and higher viscosity fluids.

Conclusion:

In summary, the correct answer to the question is option 'D' - the viscosity of the fluid. Viscosity plays a crucial role in boundary layer formation by creating a shearing effect between fluid layers and influencing the development of laminar or turbulent boundary layers. Understanding the boundary layer is essential in various fields, including aerodynamics, hydrodynamics, and heat transfer, as it significantly affects the behavior of fluid flow around solid surfaces.