Page 29 - Standard Handbook Of Petroleum & Natural Gas Engineering
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18 Mathematics
Spheroid (or ellipsoid of revolution)
By the prismoidal formula:
volume = 1/6 h(A + B + 4M)
where h = altitude
A and B = areas of bases
M = area of a plane section midway between the bases
Paraboloid of revolution (Figure 1-25)
0 #-- 7--,
# / \
volume = 1/2 nr2h = 1/2 volume of circumscribed cylinder
Torus, or anchor ring (Figure 1-26)
volume = 2n2cr2
area = 4nr2cr (proof by theorems of Pappus)
ALGEBRA
See References 1 and 4 for additional information.
Operator Precedence and Notation
Operations in a given equation are performed in decreasing order of prece-
dence as follows:
