Drag as a resistive force in fluids (5.2.1) | OCR A-Level Physics Notes

OCR Specification focus:
‘Define drag as the frictional force on objects moving through fluids; recognise dependence on speed and shape.’

Drag is a resistive force experienced by objects moving through fluids such as air or water. Understanding its causes and characteristics is essential in analysing real-world motion.

Understanding Drag as a Resistive Force

When an object moves through a fluid, the fluid exerts a force opposing the motion. This force, called drag, resists the object’s movement and converts kinetic energy into heat and turbulence within the fluid. Drag is a form of frictional force, but instead of occurring between solid surfaces, it arises due to interactions between an object and the fluid’s particles.

Nature of Drag

Drag results from two main effects:

Frictional interaction between the fluid and the surface of the moving object (viscous drag).
Pressure differences around the object due to its motion through the fluid (pressure drag).

Both effects combine to create the overall resistive force that acts opposite to the direction of motion.

Factors Influencing Drag

The magnitude of the drag force depends on several key variables that determine how a fluid interacts with a moving body.

1. Speed of Motion

Drag increases significantly with speed. At low speeds, it rises approximately in direct proportion to velocity, while at higher speeds it rises roughly with the square of velocity due to increasing turbulence and fluid displacement.

2. Shape of the Object

The streamlining of an object has a profound impact on drag. Smooth, elongated shapes reduce pressure differences and turbulence, minimising resistive effects. Conversely, irregular or blunt shapes create large wake regions, increasing pressure drag.

3. Cross-sectional Area

The larger the exposed area facing the direction of motion, the greater the drag force experienced. Reducing the frontal area is a fundamental design goal in engineering vehicles and aircraft to enhance efficiency.

4. Properties of the Fluid

The viscosity (internal friction) and density of the fluid affect the drag force. Dense or viscous fluids exert greater resistance on moving bodies. For example, movement through water experiences far higher drag than through air.

Categorising Drag Forces

Viscous Drag

Viscous drag arises from the internal friction between layers of fluid moving at different velocities around the object. It is dominant when the object moves slowly through a viscous medium, such as oil or honey.

Viscous Drag: The resistive force caused by the internal friction between adjacent layers of a fluid moving at different speeds.

Pressure Drag

Pressure drag, also called form drag, is generated by differences in pressure across the object. High pressure builds up at the front where the fluid impacts, and low pressure occurs behind as the fluid separates. This pressure imbalance pushes backward on the object.

The diagram shows how including surface friction alters the pressure distribution around a cylinder, leading to a rear pressure deficit and pressure drag. Without friction, the pressures are symmetrical and no drag acts — an idealised case known as D’Alembert’s paradox. This visual focuses only on mechanisms relevant to drag formation. Source.

These two types of drag often act together, though their relative importance varies with shape and speed.

Quantifying Drag

At higher speeds or for objects with significant cross-sectional area, drag can be approximated using an empirical equation based on experimental evidence.

EQUATION
—-----------------------------------------------------------------
Drag Force (Fₑ) = ½ Cₑ ρ A v²
Fₑ = Drag force (N)
Cₑ = Drag coefficient (dimensionless; depends on shape and surface texture)
ρ = Fluid density (kg m⁻³)
A = Cross-sectional area normal to motion (m²)
v = Velocity of the object relative to the fluid (m s⁻¹)
—-----------------------------------------------------------------

This relationship shows the quadratic dependence of drag on speed, explaining why resistance becomes dramatically stronger as an object accelerates. The drag coefficient (Cₑ) captures the combined effects of surface roughness, flow separation, and shape streamlining.

Laminar and Turbulent Flow Effects

The nature of the fluid flow around an object strongly influences drag.

Laminar flow shows smooth, parallel streamlines producing lower drag, while turbulent flow involves chaotic mixing and higher drag. The transition between these flow types depends on speed, viscosity, and object size, key factors influencing drag. Source.

Laminar Flow

Fluid particles move in smooth, parallel layers.
Occurs at low velocities or with high viscosity.
Produces less drag because there is little mixing of fluid layers.
Common for small objects moving slowly through thick fluids.

Turbulent Flow

Characterised by chaotic and irregular motion of fluid particles.
Occurs at high velocities or with low viscosity.
Causes increased drag due to eddies, vortices, and flow separation.
Typical for large or fast-moving objects, such as cars or aircraft.

The transition between laminar and turbulent flow is described by the Reynolds number, a dimensionless value comparing inertial and viscous effects. Although not required for simple OCR treatment, awareness of this concept helps explain why drag behaviour varies so markedly with speed and size.

The Role of Surface Characteristics

Surface smoothness plays an important role in determining how a fluid flows over an object.

Smooth surfaces maintain laminar flow longer, delaying turbulence.
Rough surfaces encourage early turbulence, sometimes deliberately used to control separation (e.g. dimples on golf balls reduce drag).
Coatings and finishes in vehicles and aircraft aim to minimise microscopic friction and surface irregularities.

Small modifications in surface condition can result in substantial differences in the overall drag force.

Energy Considerations

Drag converts mechanical energy into heat within the fluid. This energy loss reduces the efficiency of motion and must be overcome by a driving force such as a car engine or propeller thrust. Consequently:

The power required to maintain motion increases rapidly with speed.
Engineers design systems to minimise drag and maximise fuel or energy efficiency.

Reducing drag is vital in transport, sports, and engineering, affecting performance, cost, and sustainability.

Summary of Specification Focus

In accordance with the OCR A-Level Physics specification, drag must be defined as the frictional force on objects moving through fluids. Students must also recognise its dependence on speed and shape, understanding how factors such as flow type, surface texture, and cross-sectional area modify resistive effects. Appreciating these relationships allows accurate analysis of motion with non-uniform acceleration and underpins later study of terminal velocity and energy efficiency in moving systems.

FAQ

Drag is the general term for the resistive force experienced by an object moving through any fluid, including liquids and gases.

Air resistance is a specific type of drag that occurs when an object moves through air. While all air resistance is drag, not all drag occurs in air — for example, a ball moving through water also experiences drag.

Both depend on factors such as speed, shape, and surface characteristics, but air resistance is often smaller due to the lower density and viscosity of air compared to most liquids.

At low speeds, the flow around an object is generally smooth and laminar, producing relatively little turbulence.

As speed increases, the flow becomes turbulent — eddies, vortices, and separation zones form, greatly increasing the resistive force.

Because turbulence depends on the square of velocity, the drag force typically grows with the square of the object’s speed, making it much harder to accelerate at higher velocities.

The drag coefficient reflects how easily a shape moves through a fluid. It depends on how the shape influences flow separation and turbulence.

Typical drag coefficients include:

Smooth sphere: around 0.5
Streamlined car body: about 0.3 or lower
Flat plate perpendicular to flow: around 1.0–1.2

Streamlined shapes reduce wake size and maintain attached flow, lowering Cd, while blunt shapes cause early separation, increasing Cd.

Yes. While drag usually acts as a resistive force, it can be deliberately exploited in various ways.

Examples include:

Parachutes, which rely on high drag to slow descent safely.
Vehicle braking systems like air brakes or spoilers that increase drag for controlled deceleration.
Sports, where drag can stabilise motion — e.g., the spin and dimples on a golf ball enhance flight stability through controlled airflow.

Thus, manipulating drag can provide important control and safety benefits.

Aircraft are designed to minimise drag without compromising lift or stability. Techniques include:

Streamlined fuselage and wings to reduce pressure drag.
Smooth, polished surfaces to delay the onset of turbulence.
Winglets to limit vortex formation at wing tips.
Retractable landing gear to reduce cross-sectional area during flight.

These measures decrease fuel consumption and improve performance by ensuring that energy is not wasted overcoming unnecessary resistive forces.

Practice Questions

Question 1 (2 marks)
Define the term drag and explain how it acts on an object moving through a fluid.

Mark scheme:

1 mark: Correct definition of drag as a frictional force that opposes the motion of an object through a fluid.
1 mark: Correct explanation that drag acts in the opposite direction to the object’s velocity, resisting its motion.

Question 2 (5 marks)
A car travels at high speed along a flat road. Describe and explain how the shape, speed, and surface characteristics of the car influence the drag force acting on it.