Dynamic pressure

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In fluid dynamics dynamic pressure (indicated with q, or Q, and sometimes called velocity pressure or impact pressure) is the quantity defined by:

$q = \tfrac12\, \rho\, v^{2},$

where (using SI units):

$q\;$	= dynamic pressure in pascals,
$\rho\;$	= fluid density in kg/m³ (e.g. density of air),
$v\;$	= fluid velocity in m/s.

[edit] 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.

[edit] 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.

[edit] Alternative form

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:

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

the definition of speed of sound $v_{s}\;$ and of Mach number $M_a\;$ :

$v_{s} = \sqrt{\gamma\, R\, T}$ and $M_{a} = \frac{v}{v_{s}},$

dynamic pressure can be rewritten as:^[1]

$q = \tfrac12\, \gamma\, p\, M_{a}^{2},$

where (using SI units):

$p\;$	= pressure in pascals,
$\rho\;$	= density in kg/m³,
$R\;$	= specific gas constant (287.05 J/(kg·K) for air),
$T\;$	= absolute temperature in kelvins,
$M_a\;$	= non-dimensional Mach number,
$\gamma\;$	= non-dimensional heat capacity ratio (1.4 for air, constant),
$v\;$	= speed in m/s,
$v_s\;$	= speed of sound in m/s.