Appendix A: Drag Force

Drag force is the force exerted by a fluid, on an object, when the object moves through it. A fluid can be liquid or gas (or even something in between). So air resistance is also a drag force.

Drag is a complex phenomenon. In fact, the total drag force arises from two different causes: the inertia drag and the viscous drag.

Inertia Drag

As an object (cross-sectional area A) bulldozes its way (speed v) through a fluid (density ρ), it must “push out of the way” the fluid molecules they encounter. The rate at which forward momentum is imparted to the fluid molecules determines the magnitude of the retardation force experienced by the object (N2L and N3L). This cause of drag force is called the inertia drag Fi. It has the formula

${{F}_{i}}=\frac{1}{2}{{C}_{D}}A\rho {{v}^{2}}$

where CD is the drag coefficient, a number that depends on the shape of the object. If an object is more streamline, it has a lower CD since less fluid molecules need to be pushed forward.

Viscous Drag

The viscous drag Fv involves frictional forces between layers of fluid flowing around the object. For a spherical object with radius r, it has the formula

${{F}_{v}}=6\pi r\eta v$

where η is the viscosity of the fluid. Obviously, viscosity plays a part because there is more friction between layers of honey than say water.

Reynolds number

The ratio of inertia drag Fi to viscous drag Fv is called the Reynolds number R.

$R=\frac{{{{F}_{i}}}}{{{{F}_{v}}}}$

When R >> 1, (which typically occurs at high speed or when flow is turbulent) the inertia drag is the dominant drag force. Under such conditions, drag force D is proportional to v2.

$D=k{{v}^{2}}$

When R << 1, (which typically occurs at low speed or when flow is laminar) the viscous drag is the dominant drag force. In such conditions, drag force D is proportional to v.

$D=kv$

H2 Syllabus

The H2 syllabus only requires you to know that the drag force increases with the speed. If calculations are needed, you will be told whether to assume

$D=kv$ or $D=k{{v}^{2}}$

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