Page 659 - APPLIED PROCESS DESIGN FOR CHEMICAL AND PETROCHEMICAL PLANTS, Volume 1, 3rd Edition

A-24. A-24.

(By permission of Buffalo Tank Dir., Bethlehem Steel Corp.) ( Continued).

PROPERTIES OF THE CIRCLE AREA OF PLANE FICURES
Triangle: Base x Y2 perpendicular height.
,Fses-a) (s-h) \s-11),
Circumference c 6.28318 r - 3.14159 d s = Y2 sum of the three sides a, b and c.
Diameter c 0.31831 circumference
Area - 3.141 59 r• Trapezium: Sum of nron of the two triangles.
Trapezoid: },� sum of parallel sides x perpendicular height.
rr A
0
Arc a - 1800 - 0.017453 r A• Parallelogram: Huse x perpendicular hciaht.
1800 Regular Polygon: )'Ii 811111 of sides x inside radius.
Angle A 0 c .-r a - 57.29578 � Clrcle: 1r r• = 0.78!i·10 x din.' = 0.071)58 x circumferences
r
4 bl+ c• O
Radius r O
=-- 8 -b- Sector of Circle: � r'A = O.OU872lilir A = arc x Yi radius.
7
aeo
Chord c .. 2 ./ 2 br- bl .. 2 r aln : ( - 0)
_,---- c ,. Segment of Circle:�· � �� - sin A
Rise b • r - 'h .., 4 r1 - c• - 2 tan T 2 180
{- Circle of same area as square: d ia meter = sido x 1.128:\s
•2rainl - r+y- ./ r• - x• Square of same area as circle: side = dinrneter x 0.88fi2:�
y • b - r + .;--.,--:::::,; Elllpse: Long dinrnctcr x short din met.er x 0.78.540
x - ./ r• - (r + y - b)• Parabola: Dase x % perpendicular height.
Diameter of circle of equal periphery as squue • 1.27324 aide of equare
Side of square of equal periphery as circle - 0.78�0 diameter of circle
Diameter of circle circumscribed about square - 1.41421 side of square
Side of square inscribed in circle - 0.70711 diameter of circle -- Irregular plane surface
..
A - B
CIRCULAR SECTOR .., .. '7 c: +
c:
e
N
r =- radiu1 of circle y .. angle ncp In degree, .c ..c: .c "' .c ..c: ..c: ..c:
Area of Sector ncpo - 'h !length of arc nop X r)
a b
• Area of Circle X �
.. 0.0087266 X r• X y � --
C, - 1 I D
I I
�--- --- ---- - ----nd--------------...l
CIRCULAR SEGMENT
r = radius of circle x = chord b .a rise
Area of Segment nop=Area of Sector ncpo-Area of triangle ncp Divide 11,11y plan« i<11rfacc A, B, C. D, al<>11J!: a line rt -b into ILII cveu 1111111ber, n, of purnllo l
und aulhr-iently smnll strips, d, whos,• ordi11atcs are h,, h,, h,, h,, h, .... hn- 1, h», h 0+ 11 and
(length of arc nop X r) - x (r - b) nonsidering contours between t.hre« ordinates as pnruholie curves, then for sect ion AUCD,
2 1
Area of Segment nsp= Area of Circle - Aru of Segment nop Arca ={-[1i + hn+1+4(h,+ h, -l-h •... +h») +2(h 3 +h, ·+-h, ... +h11-,)]
or, approximately, Arna = Sum of ordinates x width, d.

VALUES FOR FUNCTIONS OF 7r
,,. = 3.14159265359, log .. 0.4971499 VOLUME OF A WEDCE
,.a - 9.8696044, log .. 0.9942998 } = 0.3183099, log = 1.5028501 � {· �0.5641896, log-1.7514251 This formula is useful in ,,I,laini11g the eon ten ts of
,... - .. - speciul, wedge-shaped, tank bottoms,
x • - 31.0062767, log � 1.4914497 _!_ - 0.1013212, log = 1.0057002 180 .. 0.0174533, log-2.2418774
..
-
180
.J,i. 1.7724S39, log - 0.2485749 � - 0.0322515, log .. 2.5085503 -;;:- • H.2957795, log-1.758122& Volume=��(]+ m + n)
(j