Druckfelder

Druckfelder, in physics and engineering, denote the spatial distribution of pressure within a medium. A Druckfeld assigns to each point in space and time a scalar value p(x, y, z, t) representing the local force per unit area exerted by the medium. In fluids, pressure contributes to the isotropic part of the Cauchy stress tensor, which can be written as σ = -p I + τ, where I is the identity tensor and τ is the viscous stress. The pressure field is constrained by the governing equations of mechanics, such as the Navier–Stokes equations for viscous fluids or the Euler equations in the inviscid limit.

In static or quasi-static situations, pressure often varies with position due to gravity and boundary conditions. For a static fluid in a gravitational field, dp/dz = -ρ g, leading to a hydrostatic pressure distribution that increases with depth. In dynamic contexts, pressure fields can propagate as waves or respond to changing boundaries. For example, in acoustics the time-dependent pressure field p(r, t) in a homogeneous medium satisfies the wave equation ∇^2 p − (1/c^2) ∂^2 p/∂t^2 = 0, where c is the speed of sound.

Measurement and application span multiple disciplines. Pressure fields are measured with transducers or manometers and are inferred from velocity and boundary conditions in fluid dynamics. They play a central role in aerodynamics, meteorology, oceanography, geophysics, and medical imaging (such as ultrasound), where transmitted or received pressure fields convey information about the medium.