The wind flows over a rough terrain and the boundary layer...

The wind flows over a rough terrain and the boundary layer is defined as $u / U=y /(y+0.01),$ where $y$ is in meters. If the free stream velocity of the wind is $18 \mathrm{~m} / \mathrm{s}$, determine the velocity at an elevation $y=0.2 \mathrm{~m}$ and at $y=0.5 \mathrm{~m}$ from the ground surface.

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Key Concepts

Free Stream Velocity

The free stream velocity represents the constant velocity of the fluid far from the effects of the boundary or obstacles. It serves as a reference point for many calculations in fluid dynamics, particularly for determining the velocity distribution within the boundary layer.

Boundary Layer

The boundary layer is a thin region adjacent to a surface in a flow field where viscous effects are significant and the velocity transitions from zero (or a lower value) at the surface to the free stream value away from the surface. It is crucial in analyzing aerodynamic friction, heat transfer, and momentum exchange between the surface and the fluid.

Velocity Profile

A velocity profile describes how the fluid velocity changes with respect to distance from a boundary. In the context of boundary layers, it often manifests as a mathematical relationship that quantifies how the velocity increases from the surface value (often zero in no-slip conditions) to the free stream velocity as the distance from the surface increases.

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