Even I know it's really hard for me to do, but I can't give up now, I need to stay focus and with Piping & Fabrication, I believe soon or later will comes the result that I want. And now lets start with Lengths, Area, Surfaces and Volume on Pipe System.
List of Symbols
A= angle, deg*
C = length of chord
d = diameter of circle or sphere = 2r
h = height of segment, altitude of cone, etc., as explained in context
π = ratio of circumference to diameter of circle = 3.1416
Φ = angle in radian measure*
S = length of arc, slant height, etc., as explained in context
r = radius of circle or sphere = d/2
R = mean radius of curvature for pipe bends
Areas are expressed in square units and volumes in cubic units of the same system in which lengths are measured.
Triangle.
Area = ½ (base) x altitude.
Circle
Circle
Area = πr² = πd²/4.
Length of arc S = Φr = 0.0175Ar.
Length of chord C = 2r sin(Φ/2) =
2r sin(A/2).
Area of Sector
Area of Segment.
Find the area of the sector having same arc and area of triangle formed by chord and radii of sector. The area of the segment equals the sum of these two areas if the segment is greater than a semicircle, and it equals their difference if the segment is less than a semicircle.
Area of Segment (method 2)
When h = 0 to ¹⁄₄d, area = h√1.766dh - h².
When h = ¹⁄₄d to ¹⁄₂d, area = h√0.017d² + 1.7dh - h².
When h = ¹⁄₂d to d, subtract area of empty sector from area of entire circle.
When h = 0 to ¹⁄₄d, area = h√1.766dh - h².
When h = ¹⁄₄d to ¹⁄₂d, area = h√0.017d² + 1.7dh - h².
When h = ¹⁄₂d to d, subtract area of empty sector from area of entire circle.
 |
| offset bends |
Offset Bends.
(See Figure) The relation of D, R, H, and L is determined by geometry for the general case shown in the Figure as follows: Consider the diagonal line joining the centers of curvature of the two arcs in either figure as forming the hypotenuse of three right-angle triangles, and write an equation between the squares of the two other sides. Thus,
Squaring both sides and solving for each term in turn, we have
where Φ = 2 tan¯¹ (HL + D) (from similarity of triangles)
When D = 0
Length of Pipe in offset :
where the angle is expressed in radians
Cylinder
where r = radius of base
h = height
Volume = πr²h
Pyramid
Right pyramid (i.e., vertex directly above center of base):
Cone
Sphere
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