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The area-equivalent radius of a 2D object is the radius of a circle with the same area as the object Cross sectional area of a trapezoidal open channel, red highlights the wetted perimeter, where water is in contact with the channel. The hydraulic diameter is the equivalent circular configuration with the same circumference as the wetted perimeter.
The ratio of the circumference of any circle to its diameter is greater than but less than . This approximates what we now call the mathematical constant π . He found these bounds on the value of π by inscribing and circumscribing a circle with two similar 96-sided regular polygons .
In 1697, David Gregory used π / ρ (pi over rho) to denote the perimeter of a circle (i.e., the circumference) divided by its radius. [ 23 ] [ 24 ] However, earlier in 1647, William Oughtred had used δ / π (delta over pi) for the ratio of the diameter to perimeter.
The circumference is the arc length of the circle, as if it were opened up and straightened out to a line segment. [1] More generally, the perimeter is the curve length around any closed figure. Circumference may also refer to the circle itself, that is, the locus corresponding to the edge of a disk.
The ratio of a circle's circumference to its diameter is π (pi), an irrational constant approximately equal to 3.141592654. The ratio of a circle's circumference to its radius is 2 π . [ a ] Thus the circumference C is related to the radius r and diameter d by: C = 2 π r = π d . {\displaystyle C=2\pi r=\pi d.}
The area of a regular polygon is half its perimeter times the apothem. As the number of sides of the regular polygon increases, the polygon tends to a circle, and the apothem tends to the radius. This suggests that the area of a disk is third the circumference of its bounding circle times the radius. [3]
A calculated perimeter is the length of fence required to surround a yard or garden. The perimeter of a wheel/circle (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool's perimeter; if the length of the string was exact, it would equal the perimeter.
Diameter (group theory), the maximum diameter of a Cayley graph of the group; Equivalent diameter, the diameter of a circle or sphere with the same area, perimeter, or volume as another object; Hydraulic diameter, the equivalent diameter of a tube or channel for fluids; Kinetic diameter, a measure of particles in a gas related to the mean free path