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The diameter of a circle is exactly twice its radius. However, this is true only for a circle, and only in the Euclidean metric . Jung's theorem provides more general inequalities relating the diameter to the radius.
The hydraulic diameter is similarly defined as 4 times the cross-sectional area of a pipe A, divided by its "wetted" perimeter P. For a circular pipe of radius R, at full flow, this is = = as one would expect. This is equivalent to the above definition of the 2D mean diameter.
In geometry, the area enclosed by a circle of radius r is πr 2.Here, the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159.
Despite what the name may suggest, the hydraulic diameter is not twice the hydraulic radius, but four times larger. Hydraulic diameter is mainly used for calculations involving turbulent flow. Secondary flows can be observed in non-circular ducts as a result of turbulent shear stress in the turbulent flow. Hydraulic diameter is also used in ...
Since the diameter is twice the radius, the "missing" part of the diameter is (2r − x) in length. Using the fact that one part of one chord times the other part is equal to the same product taken along a chord intersecting the first chord, we find that (2r − x)x = (y / 2) 2. Solving for r, we find the required result.
When a circle's diameter is 1, its circumference is . When a circle's radius is 1—called a unit circle —its circumference is 2 π . {\displaystyle 2\pi .} Relationship with π
Today's NYT Connections puzzle for Saturday, December 14, 2024The New York Times
The area of the circle equals π times the shaded area. The area of the unit circle is π. π appears in formulae for areas and volumes of geometrical shapes based on circles, such as ellipses, spheres, cones, and tori. Below are some of the more common formulae that involve π. [153] The circumference of a circle with radius r is 2πr.