Drag Force

When fluid flows around a submerged object, it generates a drag force that resist against the motion of the object. This results from two main effects: pressure distribution $p$ from the surface and shear stress distribution due to fluid viscosity (see External Flow Around Submerged Bodies).

The total drag force is the sum of two distinct contributions:

$$F_D=F_{Dp}+F_{Df}$$

where $F_{Dp}$ is the pressure drag and $F_{Df}$ is the friction drag.

• Pressure drag arises from pressure differences over the surface of the object; as fluid moves around the object, the pressure varies, creating regions of high and low pressure
• Friction drag results from shear stress (${\tau }_w$) as layers of fluid slide over each other near the surface.

The total drag force is expressed using the drag coefficient:

$$F_D=C_D\frac{1}{2}\rho V^{2}A$$

where $C_D$ is the drag coefficient, $\rho$ is the density of the fluid, $V$ is the relative velocity of the fluid with respect to the object, and $A$ is the reference area (cross-sectional or surface area depending on application).

The drag coefficient can be written as:

$$C_D=C_D\left(\text{Re},\frac{ϵ}{L},\text{shape}\right)$$

This tells us that drag coefficient depends on:

• Reynolds Number $\text{Re}$ – characterizes the flow regime (laminar or turbulent)
• Surface roughness $ϵ$ – measures how smooth or rough the surface is
• Characteristic length $L$ – The dimension that significantly influences drag (e.g., diameter for a cylinder, chord length for an airfoil).
• Shape

For a blunt cylinder:

• The flow separates easily, creating a large wake (low-pressure region
• This results in a relatively high drag coefficient: $C_D=1.2$

For a streamlined body:

• The flow stays attached longer, minimizing separation and the wake
• This reduces drag substantially, resulting in a much lower drag coefficient: $C_D=0.12$