22 BULLETIN 898, U. S. DEPARTMENT OF AGRICULTURE. 
CALCULATION OF SMALL OUTAGES ON HORIZONTAL-CYLINDRICAL TANKS AND TANK CARS. 
The outage, or empty space, in a tank car is in the form of a seg- 
ment of a horizontal cylinder, which would be formed by the segment — 
of a circle passing along the length of the car from end to end. In 
addition to this there would be a small empty space in either of the 
dished ends of the car. This is, however, almost negligible for very 
small outages, that is, 2 or 3 inches. The exact calculation of the 
outage in the dished end of a tank is very difficult, and can not be 
made by simple mathematics. Complicated charts constructed from 
the results of-involved mathematical calculations are used for this. 
For small outages up to 12 inches, 1t can be determined approximately, 
close enough for all practical purposes, by the method given on 
page 24. 
Fie. 3. 
The ‘volume of the outage in the body of the tank, in cubic inches, 
is equal to the area of the segment A (the dotted cross section in figure 
3) multiplied by the length of the car, in inches. 
For outage calculations it is simpler to consider the regular exten- 
sions of the tank heads along with the length of the body of the tank, 
rather than as parts of the tank heads. If the length of the body of 
the tank is designated by Z and the inside length of a regular exten- 
sion L,, the total cylindrical length, for the calculation of the outage 
in the body of the tank, will be equal to the sum of the length of the 
body of the tank and the two regular extensions at either end, or 
ff eles (formula 6) 
Then the main outage volume becomes 
Vi—ASGE, (formula 7) 
It is first necessary to find the value for A, by means of the formula 
rrM 0 
< (r ~h) 
(formula 8) 
A (the area of a circular segment) = 369 — > 
