Understanding the Annulus: A Versatile Mathematical Concept

In mathematics and physics, an annulus (plural: annuli) is a ring-shaped object with an inner radius and an outer radius. The term is used in various contexts, including geometry, calculus, and fluid dynamics.

In geometry, an annulus is a region bounded by two concentric circles, one inside the other. The inner circle is called the core of the annulus, while the outer circle is called the boundary. The area of the annulus is given by the difference between the areas of the inner and outer circles.

In calculus, the annulus is used to define the concept of a limit. For example, the limit of a function as the radius of an annulus approaches zero is defined as the limit of the function evaluated at the center of the annulus, divided by the distance between the center and the boundary of the annulus.

In fluid dynamics, an annulus is a type of pipe or tube that has a ring-shaped cross section. It is commonly used in heat exchangers, chemical reactors, and other industrial applications where fluids need to be mixed or heated. The inner radius of the annulus determines the size of the central channel through which the fluid flows, while the outer radius determines the size of the annular space around the central channel.

Overall, the annulus is a useful mathematical concept that has many practical applications in science and engineering.