How Does Drag Force Affect Motion in Fluids?
Drag force is a resistive force experienced by an object moving through a fluid, such as air or water. This force is always directed opposite to the object’s motion, similar to friction, but it occurs between a fluid and a solid rather than two solid surfaces.
Understanding drag force is essential in Mechanics, Fluid Friction, aerodynamics, and daily life applications. You experience drag force when you move your hand through water or feel wind resistance when cycling.
Explanation of Drag Force
The magnitude of the drag force depends on several factors: the shape and size of the object, its speed, and properties of the fluid. For most large objects moving at moderate or high velocities (like cars, balls, or skydivers), the drag force is proportional to the square of the speed.
Drag force can be mathematically expressed as:
To account for fluid and body characteristics, the full formula for drag force is:
Where:
- FD: Drag force (N)
- C: Drag coefficient (dimensionless, depends on object shape)
- ρ: Density of fluid (kg/m³)
- A: Area facing the fluid flow (m²)
- v: Velocity of the object relative to the fluid (m/s)
Drag Coefficient Values (C) for Common Objects
| Object | C (Drag Coefficient) |
|---|---|
| Airfoil | 0.05 |
| Toyota Camry | 0.28 |
| Ford Focus | 0.32 |
| Honda Civic | 0.36 |
| Ferrari Testarossa | 0.37 |
| Dodge Ram Pickup | 0.43 |
| Sphere | 0.45 |
| Hummer H2 SUV | 0.64 |
| Skydiver (feet first) | 0.70 |
| Bicycle | 0.90 |
| Skydiver (horizontal) | 1.0 |
| Circular flat plate | 1.12 |
Stokes' Law for Small Particles
For very small particles, moving slowly inside a dense medium, the drag force is directly proportional to velocity. This is given by Stokes’ Law:
Here,
- Fs: Drag force (N)
- r: Radius of the sphere (m)
- η: Dynamic viscosity of the fluid (Pa·s)
- v: Speed of the object (m/s)
Term and Applications: Terminal Velocity
When an object falls through a fluid, the drag force increases with speed. At a certain constant speed, called terminal velocity, the drag force balances the weight, and the object stops accelerating.
For large objects in air, terminal velocity (vt) can be calculated by:
Where m is mass and g is acceleration due to gravity.
Examples and Real-Life Applications
- Skydivers use body position to control drag and thus their falling speed.
- Bobsleds, cars, and airplanes are streamlined to reduce drag for higher speeds.
- Swimmers and cyclists minimize clothing drag to improve race times.
- Birds fly in a "V" formation to reduce collective drag.
Step-by-Step Approach to Solving Drag Force Problems
| Step | Action | Example |
|---|---|---|
| 1 | Write the drag force formula suitable for the problem. | FD = ½ C ρ A v² |
| 2 | Identify all known values (C, ρ, A, v, or η, r, v). | Given: C = 0.5, ρ = 1.2 kg/m³, A = 0.3 m², v = 10 m/s |
| 3 | Plug in the values with attention to units. | FD = 0.5 × 0.5 × 1.2 × 0.3 × (10)² |
| 4 | Calculate numerically to find the force. | FD = 0.5 × 0.5 × 1.2 × 0.3 × 100 = 9 N |
Practice Example
A 75 kg skydiver descends head first (A = 0.18 m², C = 0.70, ρ = 1.21 kg/m³). The terminal velocity vt is calculated by:
If the position changes to spread-eagle (A increases), terminal velocity decreases.
Type of Drag: Quadratic vs Linear
| Condition | Formula Applied | When Applicable |
|---|---|---|
| Large object, high velocity | FD = ½ C ρ A v² | Cars, balls, skydivers in air |
| Small object, low velocity, dense fluid | Fs = 6 π r η v | Bacteria, pollen, small spheres in oil/water |
Summary: Key Points on Drag Force
- Drag force opposes motion through a fluid, increasing with speed.
- It is affected by object shape, area, and fluid properties.
- For most practical cases: FD = ½ C ρ A v².
- For very small objects, Stokes’ Law applies: Fs = 6 π r η v.
- Understanding drag is essential in engineering, nature, and sports.
Glossary
- Drag Force (FD): Resistive force proportional to v² or v, opposing motion in fluid.
- Stokes’ Law: Linear drag for very small particles, Fs = 6 π r η v.
- Terminal Velocity: The constant speed when drag balances gravity during free fall.
Next Steps for Learners
- Practice problems on Drag Force.
- Explore fluid friction and terminal velocity for deeper understanding.
- Continue learning about friction, force, and motion in Physics.
Mastering drag force will help you excel in Physics exams and understand real-world engineering and biological processes better.
FAQs on What Is Drag Force? Meaning, Formula & Physics Applications
1. What is drag force in Physics?
Drag force is a type of frictional force that opposes the motion of an object as it moves through a fluid (like air or water). It acts in the direction opposite to the object's velocity relative to the fluid. For example, air resistance is the drag force that you feel when you stick your hand out of a moving car's window.
2. What are the main factors that influence the magnitude of drag force?
The magnitude of the drag force depends on several key factors:
- Velocity of the object: Drag increases significantly as the speed of the object increases. Specifically, it is proportional to the square of the velocity.
- Density of the fluid: Denser fluids, like water, exert a much greater drag force than less dense fluids, like air, at the same speed.
- Cross-sectional area: The larger the area of the object facing the fluid flow, the greater the resistance and the higher the drag force.
- Drag Coefficient (Cd): This is a dimensionless value that depends on the object's shape and surface texture. A streamlined or aerodynamic shape has a lower drag coefficient.
3. What is the formula used to calculate drag force?
The formula to calculate drag force (D) is given by the drag equation:
D = ½ × ρ × v² × A × Cd
Where:
- ρ (rho) is the density of the fluid.
- v is the velocity of the object relative to the fluid.
- A is the cross-sectional area of the object.
- Cd is the drag coefficient.
4. How does a 'streamlined shape' help reduce drag on vehicles like cars and aeroplanes?
A streamlined shape, like the teardrop design of an aircraft wing or a sports car, is designed to minimise drag. It works by allowing the fluid (air) to flow smoothly over its surface with minimal turbulence. This reduces pressure drag, which is caused by a high-pressure zone at the front and a low-pressure wake at the back. By guiding the fluid flow smoothly, a streamlined body significantly lowers its drag coefficient, improving fuel efficiency and stability at high speeds.
5. Can you provide some real-life examples of drag force?
Drag force is present in many everyday situations. For instance:
- Air resistance slowing down a moving car, bicycle, or a runner.
- A parachute uses a large surface area to maximise drag force and slow down a skydiver's descent.
- The resistance a swimmer feels when moving through water.
- The force that slows down a badminton shuttlecock, making its trajectory different from a simple ball.
6. What is the fundamental difference between drag force and lift force on an aeroplane?
The primary difference lies in their direction relative to the object's motion. Drag force always acts parallel and opposite to the direction of the aeroplane's motion through the air, resisting its forward movement. In contrast, lift force acts perpendicular to the direction of motion, pushing the aeroplane upwards and counteracting the force of gravity.
7. Why does drag force increase with the square of velocity and not just linearly?
Drag force increases with the square of velocity because at higher speeds, the object has to push aside a greater volume of fluid per second. Furthermore, the kinetic energy imparted to the fluid it displaces is proportional to v². This means that doubling your speed from 30 km/h to 60 km/h doesn't just double the drag; it quadruples it. This is why fuel consumption in vehicles increases dramatically at very high speeds.
8. What is the difference between pressure drag and skin friction drag?
These are two main components of total drag:
- Pressure Drag (or Form Drag): This is caused by the pressure difference between the front and rear of an object. A high-pressure area forms at the front where the fluid impacts the object, and a low-pressure turbulent wake forms at the back. Blunt, non-streamlined objects have high pressure drag.
- Skin Friction Drag: This is caused by the viscosity of the fluid. A thin layer of fluid sticks to the object's surface, and friction occurs between this layer and the surrounding fluid. It depends on the surface area and texture of the object.
9. What would happen if there was no drag force when objects moved through air?
In a hypothetical world without drag force (air resistance):
- A car, once accelerated, would continue moving at a constant velocity without needing continuous power from the engine (ignoring other frictions like rolling resistance).
- A parachutist would not be able to slow their descent and would continue to accelerate due to gravity.
- Projectiles like a thrown ball or a fired cannonball would travel much farther, following a perfect parabolic path as described in introductory physics.
- There would be no concept of terminal velocity, as an object would keep accelerating as long as a net force (like gravity) acts on it.
