Physical meaning

Dynamic pressure is closely related to the kinetic energy of a fluid particle, since both quantities are proportional to the particle's mass (through the density, in the case of dynamic pressure) and square of the velocity. Dynamic pressure is in fact one of the terms of Bernoulli's equation, which is essentially an equation of energy conservation for a fluid in motion. The dynamic pressure is equal to the difference between the stagnation pressure and the static pressure.
Another important aspect of dynamic pressure is that, as dimensional analysis shows, the aerodynamic stress (i.e. stress within a structure subject to aerodynamic forces) experienced by an aircraft traveling at speed $v$ is proportional to the air density and square of $v$, i.e. proportional to $q$.
Therefore, by looking at the variation of $q$ during flight, it is possible to determine how the stress will vary and in particular when it will reach its maximum value. The point of maximum aerodynamic load is often referred to as max Q and it is a critical parameter, for example, for spacecraft during launch.

Uses

The dynamic pressure, along with the static pressure and the pressure due to elevation, is used in Bernoulli's principle as an energy balance on a closed system. The three terms are used to define the state of a closed system of an incompressible, constant-density fluid.

If we were to divide the dynamic pressure by fluid density, the result is called velocity head, which is used in head equations like the one used for hydraulic head.

Compressible flow

Many authors define dynamic pressure only for incompressible flows. (For compressible flows, these authors use the concept of impact pressure.) However, some British authors extend their definition of dynamic pressure to include compressible flows.

If the fluid in question can be considered an ideal gas (which is generally the case for air), the dynamic pressure can be expressed as a function of fluid pressure and Mach number.

By applying the ideal gas law:

$p\; =\; \backslash rho\backslash ,\; R\backslash ,\; T,\backslash ,$

the definition of speed of sound $v\_\{s\}\backslash ;$ and of Mach number $M\_a\backslash ;$:

$v\_\{s\}\; =\; \backslash sqrt\{\backslash gamma\backslash ,\; R\backslash ,\; T\}$ and $M\_\{a\}\; =\; \backslash frac\{v\}\{v\_\{s\}\},$

dynamic pressure can be rewritten as:

$q\; =\; \backslash tfrac12\backslash ,\; \backslash gamma\backslash ,\; p\backslash ,\; M\_\{a\}^\{2\},$

where (using SI units):

See also

• Pressure

• Hydraulic head

• Total dynamic head

• Derivations of Bernoulli equation