Pressure gradient

A pressure gradient is the spatial rate and direction of pressure change in a medium. It drives fluid motion and contributes to forces on objects within the medium.

Pressure-gradient force: A force per unit volume exerted on a fluid because pressure varies across space. It converts this spatial pressure change into the force that drives fluid acceleration.
Pressure: The normal force exerted per unit area by a fluid or other material. A pressure gradient describes how this scalar quantity varies from place to place.
Geostrophic wind: A wind produced when the horizontal pressure-gradient force balances the Coriolis force. It is a large-scale atmospheric flow organized by horizontal pressure gradients.
Hydraulic head: The mechanical energy per unit weight of groundwater, expressed as an equivalent fluid-column height. Groundwater flow follows hydraulic-head gradients, not pressure gradients alone when elevation varies.
Navier–Stokes equations: Partial differential equations describing the motion of viscous fluids. Their momentum equation balances pressure-gradient forces against inertia, viscosity, and other forces.
Gradient: A vector of partial derivatives that points toward the steepest increase of a scalar field. Pressure gradient is the gradient operator applied to the pressure field.
Blood pressure: The pressure exerted by circulating blood on the walls of blood vessels. Differences in blood pressure along vessels provide the gradient that drives circulation.
Concentration gradient: The spatial rate and direction of change in a substance's concentration. It can drive diffusion even when pressure is uniform.
Darcy's law: A relation between fluid flow through a porous medium, its permeability, and the applied pressure difference. It quantifies how a pressure gradient drives flow through porous materials.
Scalar field: A function that assigns a scalar value to every point in a region of space. Pressure is modeled as a scalar field before its spatial variation is calculated.

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