A truck is moving with the velocity of 7 m / s and wind blows in opposite to the truck with 3

step 1 Relative air speed is the truck speed plus the opposing wind speed. So we're given the relative

A truck is moving with the velocity of 7 m / s and wind...

A truck is moving with the velocity of $7 \mathrm{~m} / \mathrm{s}$ and wind blows in opposite to the truck with $3 \mathrm{~m} / \mathrm{s}$. If the air has a temperature of $20^{\circ} \mathrm{C}$, determine the friction drag acting on the flat side $A B C D$ of the truck. Assume the boundary layer is completely turbulent.

Key Concepts

Friction Drag

Friction drag is the resistive force acting on a body due to the viscous shear stress of a fluid flowing over its surface. In aerodynamic contexts, it represents the proportion of the total drag that arises from skin friction and surface roughness rather than from pressure differences. Approaches to compute friction drag typically involve using the local or average shear stress over the surface area in contact with the fluid.

Turbulent Boundary Layer

A turbulent boundary layer is a region near the body’s surface where the fluid flow is chaotic and characterized by rapid fluctuations in velocity and pressure. This state results in a higher rate of momentum transfer compared to laminar flow, which in turn increases the friction drag. When the boundary layer is completely turbulent, standard empirical formulas and correlations are applied to estimate the friction coefficient more accurately.

Relative Velocity Considerations

Relative velocity in aerodynamic problems is the effective speed of the fluid flow as experienced by the moving object. When there is an ambient wind opposing the object’s motion, as in this scenario, the effective velocity becomes the sum of the vehicle’s speed and the opposing wind speed. This relative velocity is crucial for calculations because the dynamic pressure, which is proportional to the square of the speed, directly affects the shear stress and hence the friction drag.

Drag Coefficient

The drag coefficient is a dimensionless number that quantifies the resistance or drag of an object in a fluid environment. In cases involving friction drag, the friction drag coefficient is derived through empirical correlations that depend on factors such as surface roughness, Reynolds number, and the nature of the boundary layer. It is used in formulas that relate dynamic pressure and surface area to calculate the total drag force.

Air Properties

Air properties, such as density and viscosity, are essential in aerodynamic drag calculations. These properties can vary with temperature, and in this context, the provided temperature is used to determine the air density and kinematic viscosity. These values are necessary for calculating the Reynolds number and dynamic pressure, which are integral in evaluating friction drag on a surface.

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