a sample of completely denatured No. 5 to get through the test with no indication of the 2 per cent of methanol which it contained. Conclusions
~
Vol. 20, No. 3
INDUSTRIAL A N D ENGINEERING CHEMISTRY
322
When the procedure is strictly followed the findings are authentic for the materials for which the test was intended. By proper interpretations of the difficulties and suitable modifications, the test can be used on many other materials.
While under certain conditions confusing findings occur, these can usually be verified or eliminated by testing some of the same material to which a small quantity of methanol has been added. A method is suggested with a sensitiveness so high as to meet any requirements, but the advantages are offset by its ready response to the effect of interfering substances. The use of both methods on a sample will probably result in the detection of any methanol present, and if both give a positive indication methanol is very likely present.
Universal Tank Calibration Chart'
?
A. K. Doolittla T H E SEERWIN-~XLLIAMS Co., CHICAGO, ILL.
HE accompanying chart (Figure 2) was prepared to facilitate the work of inventorying the various liquid-
T
storage tanks used by one of the large mankfacturers of nitrocellulose lacquers. After having calibrated a number of these tanks individually, laboriously integrating the volume in the end bulges by plotting the Cross sections on COordinate paper and counting the squares, the writer determined to prepare a chart that would be applicable to all cases.
Use of Chart By use of this chart it is possible to read, with an accuracy closer than 1per cent, the volume of liquid a t any depth in a cylindrical tank, whether horizontal or vertical, of diameter 2 to 10 feet and length 1 to 50 feet. The correction for the spherical end bulges on large tanks is also plotted on the same chart. To use the chart for horizontal tanks, start at the left margin with the depth (inches) of the liquid above the bottom of the tank. Move horizontally to the right till the curve corresponding to the diameter (feet) of the tank is reached. Then move vertically till the line corresponding to the length (feet) of the tank is reached, thence horizontally to the right margin where the volume in the cylindrical portion of the tank will be read in gallons. To determine the volume in the end bulges, use the curves on the top portion of the chart. Starting at the left with the depth in inches (same as above), move horizontally to the right till the diameter curve is reached, then vertically to read the volume (both ends) on the top scale. The endbulge correction is added to the volume in the cylindrical portion to give the total volume of liquid in the tank. To use the chart for vertical tanks, consider the depth of the liquid the length of the tank. Use the full diameter of the tank, disregarding entirely the values on the left margin. The volumes in tanks of diameters or lengths not in even feet can be readily interpolated from the chart. Preparation of the Chart
A = Jh2xdy;
A =
c
This function may be integrated from: 1
Received July 2,1927.
(h-r) d r z - ( h - r ) z
to
-r + rzsin-1 h- 3rrZ r TI
but the values are more readily plotted from the data in handbooks on segment areas. The second set of curves were plotted to: V = 7.4805 AL; L = constant where V = volume (gallons), A = area (square feet), and L = length (feet).
It will be noted from the above that the abscissas common to both sets of curves represent the area of the segmental cross section of the liquid.
Volume, gallon5
Figure 1
The construction of the curves for end bulge was more interesting from the mathematical point of view. I n standard tank practice the end bulge is designed to represent a segment of a sphere of radius equal to the diameter of the tank. As the integration of the volume considered as a segment of a sphere is too complex to admit ready calculation of the values, this volume was integrated as an ellipsoid of revolution.
The main portion of the chart was prepared by plotting on logarithmic paper two sets of curves to the same abscissa. The fist set of curves were plotted to: A = f ( h ) ; D = 2r = constant where A = area (square feet), h = depth (inches), and D = diameter (feet).
x = drs-(y-r)z
V = Lhrxydz
(1)
(both ends) where
X
= :drz-(z-r)z;
Q = r(2-
