Library / Fluid Mechanics / FLU-10
Fluid Mechanics
Dynamic pressure
Pressure associated with a moving fluid.
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- FLU-10
- Rev
- v1
- Field
- Fluid Mechanics
- Result
- q [Pa]
ρ is the density of the fluid and v its speed relative to the body. q is the pressure that would be recovered if the flow were brought to rest, and it sets the scale of aerodynamic forces: lift and drag are q times an area times a coefficient. In flow with total pressure p₀ and static pressure p, q = p₀ − p.
Pressure associated with a moving fluid. It sets the scale of aerodynamic forces.
Calculator
- Dynamic pressure at twice the speed24,500 Pa
- Speed in km/h360 km/h
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 100 m/s (360 km/h) at sea level q is 6.1 kPa, about 6 % of atmospheric pressure. At 200 m/s it is 24.5 kPa, four times as much.
- Aircraft structures are limited by q rather than by speed alone, because the loads follow q. A fast, high flight can have the same q as a slow, low one.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (Pa) | Local step | Change in result |
|---|---|---|---|---|---|---|
| ρ Fluid density | 0.01 to 2,000 kg/m³ | 50 | 1e7 | 10,000,000 | +10% | +10 % |
| v Speed | 0.1 to 2,000 m/s | 0.006125 | 2,450,000 | 2,450,000 | +10% | +21 % |
Sweep of Speed
| Speed (m/s) | Dynamic pressure (Pa) |
|---|---|
| 0.1 | 0.006125 |
| 0.3448 | 0.07284 |
| 1.189 | 0.8662 |
| 4.101 | 10.3 |
| 14.14 | 122.5 |
| 48.77 | 1,457 |
| 168.2 | 17,320 |
| 580 | 206,000 |
| 2,000 | 2,450,000 |
Sweep one variable
Variables and how each one contributes
Dynamic pressure
What the equation gives you. Everything else feeds it.
Fluid density
The density of the fluid, in kg/m³ (1.225 for sea-level air at 15 °C). Directly proportional: air at altitude is thinner, so the same speed gives a lower q. Density falls by roughly 10 % per kilometre near sea level.
Speed
The speed of the flow relative to the body. Squared: doubling the speed quadruples q. A 10 % rise in v raises q by 21 %.
Worked example with the values above
- Square the speed: v² = (100)² = 10,000 m²/s².
- Multiply by half the density: ½ × 1.225 × 10,000.
- q = 6,125 Pa, which is 6.125 kPa.
Assumptions and limits
- Incompressible flow: valid for air below about Mach 0.3, where the error in q is under 2 %.
- A uniform, steady stream at a known density.
Common mistakes
- Entering the speed in km/h.
- Leaving out the factor ½.
Statistics and uncertainty
q ∝ ρ v², so a 1 % error in speed becomes 2 % in q, while 1 % in density is 1 %. Air density depends on altitude, temperature and humidity, and is usually the least well known input.
Where it is used
- Aerodynamic loads on a vehicle at a given speed and altitude.
- Dynamic pressure in a wind-tunnel or flight test.
Maths you need
- Kinetic energy: ½mv²
- Pressure: force per unit area