cylindrically

Cylindrically is an adverb derived from the adjective cylindrical. It is used to describe something that relates to a cylinder, has the shape of a cylinder, or exhibits cylindrical symmetry. The term appears in mathematics, physics, and engineering to specify properties that align with circular cross sections or axial symmetry around a central axis.

In mathematics and physics, cylindrically oriented descriptions often employ cylindrical coordinates, consisting of the radial distance r, the angular coordinate θ, and the axial coordinate z. A quantity described as cylindrically symmetric remains unchanged under rotations about a fixed axis; it may or may not depend on z, depending on the problem. Problems with circular cross sections or axial symmetry are frequently more conveniently expressed in these coordinates.

Examples of cylindrically symmetric situations include the magnetic field around an infinitely long straight wire, whose magnitude depends only on the distance from the wire; laminar flow in a straight pipe, where the velocity profile can be radially symmetric; and the stress and displacement in circular cylinders, which are often treated using cylindrically symmetric solutions. In all such cases, the dependence on the angular coordinate is eliminated, simplifying analysis.

Cylindrically is a specialized term used mainly in technical contexts. In general writing, it is more common to refer to cylindrical coordinates or cylindrical symmetry rather than the adverb form itself.