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 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 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: :\rho\frac{\partial \mathbf{u}}{\partial t} + \rho(\mathbf{u} \cdot \nabla) \mathbf{u} - \rho\nu \,\nabla^2 \mathbf{u} = - \nabla p + \rho\mathbf{g} By a
vector calculus identity (u=| \mathbf{u} |) :\nabla (u^2/2)=(\mathbf{u}\cdot \nabla) \mathbf{u} + \mathbf{u} \times (\nabla \times \mathbf{u}) so that for incompressible,
irrotational flow (\nabla \times \mathbf{u}=0), the second term on the left in the Navier-Stokes equation is just the gradient of the dynamic pressure. In
hydraulics, the term u^2/2g is known as the
hydraulic velocity head (hv) so that the dynamic pressure is equal to \rho g h_v. ==Uses==