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For a semicircle with a diameter of a + b, the length of its radius is the arithmetic mean of a and b (since the radius is half of the diameter). The geometric mean can be found by dividing the diameter into two segments of lengths a and b, and then connecting their common endpoint to the semicircle with a segment perpendicular to the diameter ...
P is the wetted perimeter of the cross-section. More intuitively, the hydraulic diameter can be understood as a function of the hydraulic radius R H, which is defined as the cross-sectional area of the channel divided by the wetted perimeter. Here, the wetted perimeter includes all surfaces acted upon by shear stress from the fluid. [3]
The hydraulic diameter is the equivalent circular configuration with the same circumference as the wetted perimeter. The area of a circle of radius R is π R 2 {\displaystyle \pi R^{2}} . Given the area of a non-circular object A , one can calculate its area-equivalent radius by setting
The perimeter of a stadium is calculated by the formula = (+) where a is the length of the straight sides and r is the radius of the semicircles. With the same parameters, the area of the stadium is A = π r 2 + 2 r a = r ( π r + 2 a ) {\displaystyle A=\pi r^{2}+2ra=r(\pi r+2a)} .
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 half the circumference of its bounding circle times the radius. [3]
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.}
A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden.
In any triangle, the distance along the boundary of the triangle from a vertex to the point on the opposite edge touched by an excircle equals the semiperimeter.. The semiperimeter is used most often for triangles; the formula for the semiperimeter of a triangle with side lengths a, b, c