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Concept
Dynamic pressure
Summary
In fluid dynamics, dynamic pressure (denoted by q or Q and sometimes called velocity pressure) is the quantity defined by:
where (in SI units):
q is the dynamic pressure in pascals (i.e., kg/(m*s2),
ρ (Greek letter rho) is the fluid mass density (e.g. in kg/m3), and
u is the flow speed in m/s.
It can be thought of as the fluid's kinetic energy per unit volume.
For incompressible flow, the dynamic pressure of a fluid is the difference between its total pressure and static pressure. From Bernoulli's law, dynamic pressure is given by
where p_0 and p_s are the total and static pressures, respectively.
Dynamic pressure is the kinetic energy per unit volume of a fluid. Dynamic pressure is one of the terms of Bernoulli's equation, which can be derived from the conservation of energy for a fluid in motion.
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.
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:
By a vector calculus identity ()
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 .
Official source
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