An airplane with the wings of width 2 m and flat surface is flying at a speed of 100 m / s. De

step 1 Okay, so let's find the properties of air at the given altitude. At an altitude of 1 km, we can

An airplane with the wings of width 2 m and flat surface is...

An airplane with the wings of width $2 \mathrm{~m}$ and flat surface is flying at a speed of $100 \mathrm{~m} / \mathrm{s}$. Determine the boundary layer thickness $\delta$ and the shear stress at the trailing or back edge. Assume the boundary layer is fully turbulent. The airplane flies at an altitude of $1.0 \mathrm{~km}$.

Key Concepts

Boundary Layer

The boundary layer is the thin region near a solid surface where viscous effects cause the fluid velocity to change from zero at the wall (due to the no?slip condition) to the free-stream velocity away from the surface. It is crucial in determining aerodynamic drag and heat transfer characteristics.

Turbulent Boundary Layer

A turbulent boundary layer is characterized by chaotic and random fluid motion, which enhances the mixing of momentum. This increased mixing leads to a thicker boundary layer compared to a laminar one and affects the distribution of shear stress along the surface.

Reynolds Number

The Reynolds number is a dimensionless parameter that represents the ratio of inertial forces to viscous forces in a fluid flow. It is used to predict flow regimes—laminar or turbulent—and determines the scaling laws for the boundary layer properties.

Shear Stress at the Surface

Shear stress at the surface is the force per unit area exerted parallel to the surface due to the fluid’s viscosity. In a turbulent boundary layer, the shear stress is influenced by increased momentum transfer from turbulent eddies and is directly related to drag and friction effects on the body.

Skin Friction Coefficient

The skin friction coefficient is a dimensionless measure of the frictional resistance due to the viscous shear stress at a surface relative to the dynamic pressure of the flow. It provides a means to quantify the drag caused by the boundary layer and is often correlated with the Reynolds number in turbulent conditions.

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