pressuregradient

Pressure gradient is the spatial rate of change of pressure within a medium. It is described by the gradient of the pressure field, denoted ∇P, and is a vector that points toward regions of higher pressure. The magnitude of ∇P indicates how rapidly pressure increases per unit distance.

In fluid dynamics, the pressure gradient is a primary force term in the momentum balance. For a fluid with density ρ and velocity v, the acceleration is influenced by the pressure gradient and other forces via ρ dv/dt = -∇P + μ∇^2 v + ρ g. Hydrostatic balance in a fluid at rest gives ∇P = ρ g, so pressure increases with depth. The vertical pressure gradient ∂P/∂z equals ρ g (sign depends on the coordinate convention). The horizontal gradient ∂P/∂x, ∂P/∂y drives horizontal flow.

In meteorology and oceanography, horizontal pressure gradients drive winds and currents. When balanced with the Coriolis force, the flow becomes geostrophic: f k × v = - (1/ρ) ∇P_h, where ∇P_h is the horizontal pressure gradient. Stronger gradients yield stronger winds; gradient strength and direction vary with weather systems, density stratification, and rotation.

In acoustics, pressure gradients govern the acceleration of particles and the propagation of sound; in fluid dynamics, they are central to wave propagation and dynamic pressure effects. Practically, the gradient is computed from measured or simulated pressure fields to analyze flows, waves, or atmospheric conditions.

See also: pressure, gradient, hydrostatics, Navier–Stokes equations, geostrophic wind.