CALCULATION OF THE VOLUME OF LIQUID CONTAINED IN A PARTIALLY-FILLED RIGHT CIRCULAR CYLINDER INCLINED TO THE HORIZONTAL Page: 4 of 7
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CALCULATION OF THE VOLUME OF LIQUID CONTAINED
IN A PARTIALLY-FILLED RIGHT CIRCULAR
CYLINDER INCLINED TO THE HORIZONTAL
Estimation of the volume contained in an inclined partially-filled
cylindrical vessel (such as the HRT dump tanks) may be considerably simplified
by use of the curve shown in Fig. 2. Consider the profile view of a circular
cylinder shown in Fig. 1.
Fig. 1 - Partially-Filled Cylinder
The volume of a solid such as is represented by the shaded area is
given by the formula:
V = R3 (0 - 2 ) sin 0 + cos 0 - cos3 (1)
tan L 2. 3
where 0 = sin-1 (R - d sec e) and -n/2 2 (2)
This is the volume having one base which is cut off by a plane which passes
through an edge of one base of a finite right circular cylinder and inter-
sects the opposite face. (Note that if the plane passes through the cylinder
"diagonally," i.e., sec 6 = 2R/d, the formula gives
V = R3 -2x - 1+ 0 -2x -1 - s 2
2 R/H L 22
The function in the brackets, F(O) = 0 sin 0 + cos 0 - sin 0 - 3 cos3
is plotted in Fig. 2 against sin 0. After calculating sin 0 from the angle @,the
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Tobias, M. CALCULATION OF THE VOLUME OF LIQUID CONTAINED IN A PARTIALLY-FILLED RIGHT CIRCULAR CYLINDER INCLINED TO THE HORIZONTAL, report, May 19, 1955; Oak Ridge, Tennessee. (digital.library.unt.edu/ark:/67531/metadc1020622/m1/4/: accessed October 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.