At a stagnation point the dynamic pressure is equal to the difference between the stagnation pressure and the static pressure, so the dynamic pressure in a flow field can be measured at a stagnation point.[1]
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 travelling at speed is proportional to the air density and square of , i.e. proportional to . Therefore, by looking at the variation of 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 in many applications, such as launch vehicles.
Dynamic pressure can also appear as a term in the incompressible Navier-Stokes equation which may be written:
so that for incompressible, irrotational flow (), the second term on the left in the Navier-Stokes equation is just the gradient of the dynamic pressure. In hydraulics, the term is known as the hydraulic velocity head (hv) so that the dynamic pressure is equal to .
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.
When the dynamic pressure is divided by the product of fluid density and acceleration due to gravity, g, the result is called velocity head, which is used in head equations like the one used for pressure head and hydraulic head. In a venturi flow meter, the differential pressure head can be used to calculate the differential velocity head, which are equivalent in the adjacent picture. An alternative to velocity head is dynamic head.
Compressible flow
Many authors define dynamic pressure only for incompressible flows. (For compressible flows, these authors use the concept of impact pressure.) However, the definition of dynamic pressure can be extended to include compressible flows.[2][3]
For compressible flow the isentropic relations can be used (also valid for incompressible flow):
"the dynamic pressure is equal to half rho vee squared only in incompressible flow." Houghton, E.L. and Carpenter, P.W. (1993), Aerodynamics for Engineering Students, Section 2.3.1
This article uses material from the Wikipedia article Dynamic_pressure, and is written by contributors.
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