Calculation
q = ½ · ρ · v²
Calculate dynamic pressure q, flow velocity v or fluid density ρ using q = ½ρv². Dynamic pressure rises with the square of velocity and is the reference quantity of many loss models.
q = ½ρv²
Dynamic Pressure Calculator
Calculate dynamic pressure q, flow velocity v or fluid density ρ using q = ½ρv². Dynamic pressure rises with the square of velocity and is the reference quantity of many loss models.
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Result
Select a target and calculate.
Dynamic pressure q versus flow velocity v
q = ½·ρ·v² rises with the square of the velocity: doubling the speed quadruples the dynamic pressure. The density ρ stays at the entered value.
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Understand the inputs
- Dynamic pressure q — The dynamic pressure (stagnation pressure) – the extra pressure that appears when a flowing liquid or gas is brought fully to rest (e.g. at a pitot tube). Computed as a result from ½·ρ·v².
- Density ρ — The density of the flowing fluid. Source: a material table (water ≈ 1000 kg/m³, air at 20 °C and standard pressure ≈ 1.2 kg/m³).
- Flow velocity v — The flow velocity, averaged over the considered cross-section. Source: a measurement (e.g. pitot tube, vane anemometer), or computed from Q/A.
Example
Water at 1 m/s: q = 500 Pa.
Assumptions and limits
Incompressible flow; local velocity profiles are averaged.
Understand Dynamic Pressure Calculator
This dynamic pressure calculator finds the missing quantity among dynamic pressure q, fluid density ρ and flow velocity v from the other two using q = ½ρv². Using the pitot tube as an example, it shows how aircraft and vehicles actually determine speed from a pressure measurement.
What does this quantity describe?
Dynamic pressure is the portion of a flow's total pressure attributable to its motion: q = ½·ρ·v². It grows with the square of velocity and is the difference between total (stagnation) pressure and static pressure.
A pitot tube on an aircraft measures the total pressure of the oncoming air, while separate static ports capture undisturbed ambient pressure. The difference between the two is exactly dynamic pressure q, from which the airspeed indicator derives displayed speed via q = ½·ρ·v² — the higher the airspeed, the larger the measured pressure difference.
Dynamic pressure symbol and formula
Symbol: q (hydraulics texts also write p_dyn). Unit: pascal, 1 Pa = 1 N/m². Formula: q = ½·ρ·v², with ρ = fluid density in kg/m³ and v = flow velocity in m/s. Dynamic pressure is the velocity term of the Bernoulli equation: static pressure p + dynamic pressure ½ρv² = total (stagnation) pressure. At the stagnation point of an obstacle the velocity drops to zero and the dynamic term appears as stagnation pressure; in duct and ventilation practice the same quantity is also called velocity pressure. The relationship holds for incompressible flow (ρ = const.).
Formula and variables
q = ½ · ρ · v²
q = ½ · ρ · v²v = √(2q/ρ)ρ = 2q/v²
| Symbol / input | Meaning |
|---|---|
| Dynamic pressure q | The dynamic pressure (stagnation pressure) – the extra pressure that appears when a flowing liquid or gas is brought fully to rest (e.g. at a pitot tube). Computed as a result from ½·ρ·v². |
| Density ρ | The density of the flowing fluid. Source: a material table (water ≈ 1000 kg/m³, air at 20 °C and standard pressure ≈ 1.2 kg/m³). |
| Flow velocity v | The flow velocity, averaged over the considered cross-section. Source: a measurement (e.g. pitot tube, vane anemometer), or computed from Q/A. |
Choose the inputs correctly
Enter two of the three quantities. Dynamic pressure requires density and velocity, velocity requires dynamic pressure and density (via a square root), density requires dynamic pressure and velocity.
How to use the calculator
Select the target quantity and enter the two known values with units. For air flows, use density at the actual altitude and temperature, since it noticeably affects calculated velocity for a given pressure.
Worked example
Given ρ = 1,000 kg/m³ (water) and v = 1 m/s, substitution gives q = 0.5 · 1,000 · 1² = 500 Pa.
Understand the result and units
A dynamic pressure of 500 Pa shows the velocity-related pressure component of this flow. Since q grows with the square of v, doubling velocity to 2 m/s quadruples dynamic pressure to 2,000 Pa.
The SI unit is the pascal (Pa = N/m²). Density is given in kg/m³, velocity in m/s; for air at standard conditions, ρ ≈ 1.225 kg/m³ is often used.
Typical applications
Dynamic pressure is used to measure vehicle and aircraft speed with pitot tubes, to design wind loads on structures, in vehicle and aircraft aerodynamics, and as the reference quantity for pressure-loss and drag coefficients in pipe flow: losses are expressed as ζ·½ρv², a multiple of the dynamic pressure. Dubbel gives the stagnation pressure of a 100 km/h wind on a wall as about 464 N/m² (ρ = 1.2 kg/m³) – reproducible with this calculator or the Bernoulli equation calculator.
Assumptions, limits and common mistakes
The formula assumes incompressible flow. At high speeds in gases, particularly near or above the speed of sound, air compressibility must be accounted for, and the simple formula q = ½ρv² becomes increasingly inaccurate.
Common mistake: Do not confuse dynamic pressure with static or total pressure — a pitot tube first measures total pressure; dynamic pressure results only as the difference against separately measured static pressure. Also, for air flows, don't assume sea-level density uncritically when actually measuring at high altitude or a different temperature.
Frequently asked questions
How does an aircraft's airspeed indicator determine speed?
From the difference between total pressure measured by the pitot tube and static pressure measured separately. That difference is dynamic pressure, from which speed follows via q = ½ρv².
Why does dynamic pressure quadruple at double the speed?
Because velocity enters the formula squared. Doubling v quadruples v² and therefore q.
Why do aircraft explicitly account for air density?
Because air density falls noticeably with altitude. At the same measured dynamic pressure, lower density at high altitude means a higher actual velocity.