Library / Fluid Mechanics / FLU-11
Fluid Mechanics
Drag force
Resistance of a fluid to a moving body.
- Ref
- FLU-11
- Rev
- v1
- Field
- Fluid Mechanics
- Result
- FD [N]
ρ is the fluid density, v the speed relative to the fluid, C_D the drag coefficient and A the reference area that the coefficient was defined with (usually the frontal area for a vehicle). F_D acts opposite to the motion. The force is ½ρv² multiplied by C_D A, so it is dynamic pressure times an effective area.
Resistance of a fluid to a moving body. It grows with the square of speed, so the power needed grows with the cube.
Calculator
- Power to overcome the drag, F_D v45.94 kW
- Drag at twice the speed3,675 N
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- At 50 m/s (180 km/h) this body feels 919 N, and overcoming it takes 46 kW. At 100 m/s the force is 3.7 kN and the power 368 kW, eight times more.
- Because power rises as v³, a small increase in top speed costs a lot of engine: 26 % more speed needs about double the power.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (N) | Local step | Change in result |
|---|---|---|---|---|---|---|
| ρ Fluid density | 0.01 to 2,000 kg/m³ | 7.5 | 1,500,000 | 1,500,000 | +10% | +10 % |
| A Reference area | 0.001 to 1,000 m² | 0.4594 | 459,400 | 459,400 | +10% | +10 % |
| v Speed | 0.1 to 1,000 m/s | 0.003675 | 367,500 | 367,500 | +10% | +21 % |
| CD Drag coefficient | 0.01 to 2 | 30.63 | 6,125 | 6,094 | +10% | +10 % |
Sweep of Speed
| Speed (m/s) | Drag force (N) |
|---|---|
| 0.1 | 0.003675 |
| 0.3162 | 0.03675 |
| 1 | 0.3675 |
| 3.162 | 3.675 |
| 10 | 36.75 |
| 31.62 | 367.5 |
| 100 | 3,675 |
| 316.2 | 36,750 |
| 1,000 | 367,500 |
Sweep one variable
Variables and how each one contributes
Drag force
What the equation gives you. Everything else feeds it.
Fluid density
The density of the fluid, in kg/m³. Directly proportional: the same shape in water feels about 800 times the drag it feels in air at the same speed.
Speed
The speed relative to the fluid. Squared: doubling the speed quadruples the force, and the power needed to overcome it is cubed. A 10 % rise in v raises F by 21 %.
Drag coefficient
The drag coefficient, a number set by the shape and Reynolds number. Directly proportional: halving the drag coefficient halves the force at any speed.
Reference area
The reference area on which C_D is based, in m². Directly proportional: a larger frontal area gives proportionally more drag.
Worked example with the values above
- Dynamic pressure: ½ρv² = ½ × 1.225 × 50² = 1,531 Pa.
- Effective area: C_D A = 0.3 × 2 = 0.6 m².
- FD = 1,531 × 0.6 = 918.8 N.
Assumptions and limits
- Steady flow at a constant C_D, which changes with Reynolds number and, near the speed of sound, with Mach number.
- The reference area is the same one used to define the quoted C_D.
Common mistakes
- Using C_D with the wrong reference area (frontal area for a car, wing area for an aircraft).
- Forgetting that power depends on the cube of the speed.
Statistics and uncertainty
F ∝ ρ v² C_D A, so the speed dominates: a 1 % error in v gives 2 % in F, against 1 % for each of the others. C_D itself is rarely known to better than 5 to 10 %, and varies with Reynolds number, yaw angle and surface condition.
Where it is used
- Estimating vehicle drag and the engine power needed to overcome it.
- Predicting the speed at which a falling body reaches terminal velocity.
Maths you need
- Dynamic pressure: ½ρv²
- Dimensionless coefficients: a number set by shape