20 BULLETIN 898, U. S. DEPARTMENT OF AGRICULTURE. 
In order, then, to accurately determine the volume of such a tank 
head, the volume of the cylindrical regular extension, as well as that — 
of the dished or spherical portion, must be calculated. The volume 
of the regular extension is determined in the same way as the body of 
the tank (p. 17), using the proper value for the inside diameter. To 
calculate the dished portion, it is first necessary to determine the 
net depth, inside, of the dished portion, which can be done by means 
of the formula, 
6b =R— JR? 7? (formula 3) 
in which 
b =net inside depth of dishing or bilge, in inches. 
R=120 inches, or the radius of the sphere, of which the dished 
end is a segment. 
r =radius of the base of this segnemt, or one-half the ede 
diameter of the regular extension, in inches. 
Having determined the value of 6, in inches, for the size tank under 
consideration, it should be applied to the formula for determining the 
volume of a spherical segment, thus, 
Vp =0.5236 x bx (37? +6?) (formula 4) 
in which | 
V,= volume of the spherical segment, 1. e., the tank end, in cubic 
inches. 
b=depth of dishing or bilge. 
r=radius, or one-half the inside diameter of the tank. 
Since a gallon (United States liquid measure) contains 231 cubic 
inches, the value for V, thus obtained must be divided by 231 to give 
the volume of the dished part of the tank end, in gallons. The 
formula then becomes 
2 2 
Volume (in gallons) ee 
The total capacity of the dome pockets depends on the diameter of 
the dome and the diameter of the tank on which the dome rests. 
Some of the usual cases are given in Table 3. 
TABLE 3.—Dome pocket capacity. 
Total Total Total 
Diam- | Diam- | capac- | Diam- | Diam- | capac- | Diam- | Diam- | capac- 
ater of | eter of | ity of | eter of | eter of | ity of | eter of | eter of | ity of 
dome. | tank. | dome | dome. | tank. | dome | dome. | tank. | dome 
‘pockets. pockets. pockets. 
Inches. | Inches. \|Galions.| Inches. | Inches. |Gallons.| Inches. | Inches. |Gallons. 
30 74 253 44 60 14.0 54 724 26.0 
32 68 Sao 44 68 12.0 54 78 24.5 
32 78 2.8 44 78 10.0 54 83 nO) 
36 62 5.0 44 864 9.0 58 894 20. 0 
42 80 9.0 52 78 21.0 58 783 28.0 
12 83 8.0 52 863 19.0 
