动态压力

The concept of dynamic pressure originates from the conservation of energy for a moving fluid. It represents the portion of the fluid’s total energy associated with its bulk motion. The formula [latex]q = \frac{1}{2} \rho u^2[/latex] can be derived by considering the kinetic energy ([latex]E_k = \frac{1}{2} m u^2[/latex]) of a small parcel of fluid with mass [latex]m[/latex] and volume [latex]V[/latex]. Since density [latex]\rho[/latex] is mass per unit volume ([latex]\rho = m/V[/latex]), the kinetic energy per unit volume is [latex]E_k/V = (\frac{1}{2} m u^2)/V = \frac{1}{2} (m/V) u^2 = \frac{1}{2} \rho u^2[/latex]. This result shows that dynamic pressure is not a pressure in the conventional sense of a normal force per unit area exerted by molecular collisions (which is static pressure). Instead, it is a scalar quantity with units of pressure (Pascals in SI units) that conveniently represents the kinetic energy density of the flow. This distinction is crucial; dynamic pressure cannot be measured directly by a standard pressure gauge oriented parallel to the flow. It can only be measured by bringing the fluid to a stop isentropically, converting its kinetic energy into a measurable pressure increase.

Historically, the groundwork was laid by Daniel Bernoulli in his 1738 work *Hydrodynamica*. While he formulated the overarching principle of energy conservation in fluids, the explicit isolation and naming of “dynamic pressure” as a distinct term became more common with the development of modern fluid dynamics and aerodynamics in the late 19th and early 20th centuries. Its utility lies in simplifying complex fluid dynamics equations. For instance, in many aerodynamic calculations, the forces are non-dimensionalized using dynamic pressure, which allows for the comparison of aerodynamic performance of different-sized objects at different speeds and in different fluids, as long as other parameters like the 雷诺数 are matched. This makes it a cornerstone quantity for wind tunnel testing and computational fluid dynamics (CFD).