tangentialPressure

TangentialPressure refers to the component of pressure that acts in directions tangent to a surface, as opposed to the normal pressure that acts perpendicular to the surface. In an ideal, isotropic fluid, pressure is the same in all directions and effectively acts normal to boundaries, so a separate tangential pressure is not present. Tangential pressure becomes meaningful in systems with anisotropic stress, curved geometries, or selective boundary conditions.

In continuum mechanics terms, the traction on a surface with unit normal n is t = σ · n, where σ is the Cauchy stress tensor. The normal stress on the surface is p_n = t · n = n_i σ_ij n_j. The tangential component of the traction is t_t = t − p_n n, whose magnitude describes the shear or tangential stress at the surface. In some contexts, especially for anisotropic materials, the tangential component is informally referred to as tangential pressure, though strictly it is a tangential traction or shear stress component.

In contexts such as general relativity and astrophysics, tangentialPressure is used to describe anisotropic pressures in fluids. For a spherically symmetric, anisotropic fluid, the stress-energy tensor can be written with radial pressure p_r and tangential pressure p_t, where p_t applies to the angular directions θ and φ. This tangential pressure influences the internal equilibrium and stability of objects like stars, entering generalized hydrostatic equations.

Examples of relevance include membranes, thin shells, and astrophysical models where directional stresses differ. In many ordinary fluids under calm conditions, tangential stresses are dominated by shear and are not described as a separate pressure, but the concept remains important for analyzing anisotropic or curved-surface systems.