Page 27 - Standard Handbook Of Petroleum & Natural Gas Engineering

16 Mathematics

9 Hollow sphere, or spherical shell
volume = 4/3 z(R3 - r3) = 1/6 x(D3 - d3) = 4xR;t + 1/3 ztq
where R,r = outer and inner radii
D,d = outer and inner diameters
t = thickness = R - r
R, = mean radius = 1/2 (R + r)

Any spherical segment (Zone) (Figure 1-21)

volume = 1/6 sch(3a2 + 3a: + h2)
lateral area (zone) = 2nrh
where r = radius of sphere

Spherical sector (Figure 1-22)

volume = 1/3 r area of cap = 2/3 m2h
total area = area of cap + area of cone = 2xrh + ma
Note: as = h(2r - h)