Hydrodynamic Boundary Layer Thickness

The hydrodynamic boundary layer thickness is a crucial parameter in fluid mechanics that characterizes the behavior of fluid flow near a solid surface. This thickness is defined as the distance from the surface where the velocity equals 99% of the local external velocity.

Understanding the Hydrodynamic Boundary Layer

In fluid flow over a solid surface, the presence of viscosity causes the fluid to adhere to the surface. This creates a thin layer of fluid, known as the boundary layer, where the velocity of the fluid changes from zero at the surface to the external velocity of the flow.

The hydrodynamic boundary layer can be divided into two regions: the laminar boundary layer and the turbulent boundary layer. In the laminar boundary layer, the fluid flows smoothly in parallel layers, while in the turbulent boundary layer, the flow becomes chaotic and irregular.

The hydrodynamic boundary layer thickness is an important parameter because it determines the extent of the flow separation and the resistance to the fluid flow. Understanding this thickness helps engineers analyze the pressure distribution, drag force, and heat transfer in various applications, such as aerodynamics, pipe flow, and heat exchangers.

Determining the Hydrodynamic Boundary Layer Thickness

The hydrodynamic boundary layer thickness can be determined using different criteria, such as velocity, momentum, or displacement thickness. In this case, the correct answer is option 'D', where the velocity equals 99% of the local external velocity.

This criterion is based on the observation that at a distance from the surface, the fluid velocity approaches the external velocity of the flow. By considering 99% of the local external velocity, a reasonable distance from the surface is chosen to define the hydrodynamic boundary layer thickness.

Significance of the Chosen Criterion

The choice of using 99% of the local external velocity is somewhat arbitrary but practical. This criterion ensures that a sufficient distance from the surface is considered, where the velocity has reached a significant portion of the external velocity. Additionally, using a high percentage like 99% provides a conservative estimate, allowing for a more accurate characterization of the flow behavior.

By defining the hydrodynamic boundary layer thickness as the distance where the velocity equals 99% of the local external velocity, engineers can analyze and predict the flow behavior near solid surfaces. This information is crucial for designing efficient and effective systems involving fluid flow, such as aircraft wings, ship hulls, and heat exchangers.