The hydrodynamic boundary layer thickness is defined as the distance from the surface where the

Explanation:

Hydrodynamic Boundary Layer:

• The hydrodynamic boundary layer is the thin region adjacent to a solid surface where the effects of viscous forces are significant, and the fluid velocity changes from zero (due to the no-slip condition at the solid surface) to approximately the free stream velocity of the fluid. The boundary layer thickness is a key parameter in fluid dynamics and is often used to understand flow behavior near surfaces.

Boundary Layer Thickness:

• The boundary layer thickness is defined as the distance from the surface where the velocity of the fluid reaches a specific percentage (typically 99%) of the free stream velocity. This definition helps to quantify the region affected by viscous forces and is crucial for analyzing drag, heat transfer, and other flow-related phenomena.
• The hydrodynamic boundary layer thickness is the distance from the solid surface where the velocity of the fluid reaches 99% of the local external velocity (also referred to as the free stream velocity). The local external velocity is the velocity of the fluid outside the boundary layer, where viscous effects are negligible, and the flow can be approximated as inviscid.

Mathematical Representation:

Let u represent the velocity of the fluid at a distance y from the surface, and U represent the free stream velocity (local external velocity). The boundary layer thickness, denoted by δ, is defined such that:

u = 0.99 × U at y = δ

This equation indicates that the velocity at the edge of the boundary layer is 99% of the free stream velocity. Beyond this point, the effects of viscosity are negligible, and the velocity remains nearly constant at the free stream value.

Applications:

• Analyzing drag forces on vehicles, aircraft, and ships to improve aerodynamic and hydrodynamic performance.
• Designing heat exchangers and optimizing heat transfer in thermal systems.
• Predicting flow separation and its impact on lift and drag in aerodynamic surfaces.
• Studying pollutant dispersion in environmental engineering and modeling fluid flow in natural systems.