Dynamic Pressure⚠ unverified
Physics / Fluids · q = ½ ρ v²
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| density | ρ | kg/m^3 | 1.225 | Fluid density (air at sea level) |
| velocity | v | m/s | 10.0 | Flow velocity |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| dynamic_pressure | q | Pa | Dynamic pressure |
The science & history
Understanding the Parameters
-
$\rho$ — air ≈ 1.225 kg/m³ at sea-level ISA; water ≈ 1000 kg/m³. Higher density → higher $q$ at the same speed.
-
$v$ — $q$ scales as $v^{2}$: double speed, quadruple dynamic pressure (and aerodynamic loads).
- $q$ — has units of pressure; in Bernoulli’s equation it is the $\tfrac12\rho v^{2}$ term.
Derivation (Approaching a Proof)
Kinetic energy of a fluid parcel of volume $\mathcal{V}$ is $\tfrac12 (\rho\mathcal{V}) v^{2}$. Energy per unit volume is therefore $\tfrac12\rho v^{2}$. That quantity has the same dimensions as pressure and is defined as dynamic pressure $q$. From steady Bernoulli along a streamline (incompressible),
$$p + \tfrac12\rho v^{2} + \rho g h = \mathrm{const},$$
so $q$ is the convertible kinetic contribution (see Bernoulli Total Pressure).
History
Dynamic pressure is standard in aerodynamics (pitot-static airspeed, load factors) and pipe flow. $q$ appears throughout aircraft structural and performance analysis.
Related Concepts: Bernoulli Total Pressure, Lift, Drag, Reynolds Number, Mach Number
Notes: Registry calculators dynamic-pressure (Fluids) and Aerospace duplicates share this page
(unverified). Incompressible / ideal definition; compressible impact pressure needs isentropic
relations.