LTR: Fluid Drag

Not surprisingly, as a fluid flows past a solid object it exerts a force on the solid. There are several classes of force typically discussed in fluid mechanics, but the two most common are drag and lift.

$\displaystyle{\vec{F_T} = -\int_A P\vec{n}dA + \int_A \vec{\tau_w} dA}$

DEFINITION:

The drag force is the component of the force from the fluid on the solid that is in the direction parallel to the flow (here denoted as the x direction).

$D \equiv \vec{F_T} \bullet \vec{e_x}$

DEFINITION:

The lift force is the component of the force from the fluid on the solid that is in the direction perpendicular to the flow (here denoted as the y direction).

$L \equiv \vec{F_T} \bullet \vec{e_y}$

In both the case of drag and lift the forces arise from two sources: fluid friction (viscous forces), and non-uniform pressure distributions (pressure forces).

NOTE:

Lift forces are only very weakly dependent on friction. they are primarily pressure-derived forces.

The components of the drag force that arise from friction and pressure are given "special names":

DEFINITION:

The skin drag/friction is the portion of the drag force that arises due to shear stresses (viscous effects).

DEFINITION:

The form drag is the portion of the drag force that arises due to normal stresses (pressure effects).

As the above equations would imply, the components of the drag may be analytically calculated if the pressure and shear stress distributions are known (and we will do this later); however, in many cases, these calculations are difficult and experimental measurements of these components are useful alternatives.

OUTCOME:

Distinguish between lift, drag, skin friction, and form drag.