Page 22 - Standard Handbook Of Petroleum & Natural Gas Engineering

Geometry 11

where rad A = radian measure of angle A
For small arcs,
-
s = 1/3 (8~‘ C)
where c’ = chord of half of the arc (Huygen’s approximation)
Note: c = 22/ho

c’ = Jdh or d = d2/h
where d = diameter of circle
h = r[l - cos (1/2 A)]
s = 2r rad (1/2 A)
Ellipse (Figure 1-12)

area of ellipse = nab
area of shaded segment = xy + ab sin-’ (x/a)
length of perimeter of ellipse = x(a + b)K,
where K = (1 + 1/4 m2 + 1/64 m4 + 1/256 m6 + . . .)
m = (a - b)/(a + b)
For m = 0.1 0.2 0.3 0.4 0.5
K = 1.002 1.010 1.023 1.040 1.064
For m = 0.6 0.7 0.8 0.9 1 .0
K = 1.092 1.127 1.168 1.216 1.273
Hyperbola (Figure 1-13)