Page 157 - Standard Handbook Of Petroleum & Natural Gas Engineering

142 General Engineering and Science

The weight W of the body acts at the center ofgruuity, the Cartesian coordinates of
which are found by:

1
7 = -jydw
W"
1
Z = - zdw
W

The foregoing are volume integrals evaluated over the entire volume of the rigid
body and dw is an infinitesimal element of weight. If the body is of uniform density,
then the center of gravity is also called the centroid. Centroids of common lines,
areas, and volumes are shown in Tables 2-1, 2-2, and 2-3. For a composite body made
up of elementary shapes with known centroids and known weights the center of
gravity can be found from

(2-10)

(2-1 1)

Table 2-1
Centroids of Common Lines [2]