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tating to venture into the field of radium therapy. The result, practically, is to confirm the National Radium Institute in a monopoly of radium for therapeutic purposes. Legislation in regard to the Government radium lands is again pending and it seems more than a coincidence that Bulletin 104should appear with its glitter of cheap radium-at this moment. STANDARD CHEMICAL COXPANY CHARLESH. VIOL PITTSBURGH, February 16, 1916
COMMENTS ON “GAUGING OF STORAGE TANKS”’ Editor of the Journal of Industrial and Engineering Chemistry: We have studied the above-mentioned article by Mr. Ogden with a great deal of interest. There is certainly a very real need of a simple and accurate method of gauging the volume of material contained in these storage tanks. Such a method should take account of the material contained in the bumped heads, should be reasonably accurate and should be simple and easy to apply. The writer is inclined to be of the opinion, however, that Mr. Ogden’s method scarcely meets this need satisfactorily, basing this opinion upon the following features of Mr. Ogden’s method: ( I ) lack of accuracy, ( 2 ) lack of simplicity or general applicability. DESCRIPTION OF METHOD
Mr. Ogden treats the contents of the tank as consisting of two component parts, ( I ) the content of material in the cylindrical portion of the tank, i. e., the tank exclusive of the bumped heads, and ( 2 ) the content of material held by the bumped heads. By determining the values of these component volumes for each vertical inch of height and adding them together, Mr. Ogden obtains the total content of material for each vertical inch of height. This amounts t o a virtual calibration of the tank for each inch of height. In discussing this article, we shall endeavor to follow this method of Mr. Ogden in treating the two-component volumes separately and we shall designate them as Vol. A (volume of cylindrical tank) and Vol. B (volume of a single bumped head). Then Total Vol. = Vol. A 2 Vol. B Volume A is equal to the product of the length of the tank and the cross-sectional area of the liquid formed in a plane perpendicular to the axes of the tank. This cross-sectional area is the segment of a circle. Mr. Ogden correctly states that its value can be obtained by integral calculus but that a simpler method consists in the use of trigonometry and geometry. Mr. Ogden seems to feel, however, that the latter method is still too complex for his purposes and he, therefore, adopts an approximation consisting substantially as follows: Vol. A is considered as consisting of a number of flat slabs I in. thick, of trapezoidal cross-section, and piled one upon the other. Mr. Ogden obtains by geometry the value of the medial line of each trapezoid. Multiplying this value in inches by the length of the tank in inches, he obtains the volume of each slab. Adding the volumes of these slabs, he obtains the varying values for Vol. A . Clearly this is quite cumbersome and only an approximation with its degree of accuracy dependent upon the ratio of the “unit of calibration” (in this case I in.) to the total qiameter of the tank. If the value of this ratio is small, the inaccuracy introduced is not very considerable. On the other hand, if this ratio is large, the method becomes very inaccurate. Regardless, however, of the degree of accuracy attained, there scarcely seems to be a very real need of a method of approximation since we have very accurate Engineering Tables which give accurately the area of
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element, and, besides these there are 10 institutlons and physicians that possess 100 or more mg., and 16 that have 50 or more mg available. The results in radium therapy reported by these institutions and physicians show that the quality of their work compares favorably wlth the work in institutions where over a gram of radium is available. the number of patients treated, of course, being smaller. 1 R.
I. Ogden, THISJOURNAL. 8 (1916), 58.
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the circular segment from a knowledge of the ratio of its height to the diameter of the circle.1 In determining Volume B there is more warrant for an approximation since no method has apparently up to the present time been published which gives this volume content accurately. Vol. B consists of a portion of the segment of a sphere. Mr. Ogden treats the radius of this sphere as equal to the diameter of the tank which assumption, in view of the practice of tank design, is essentially correct. Mr. Ogden’s method of determining Vol. B is substantially as follows: Volume B is considered as consisting of a number of I in. slabs piled one upon the other. Through the center of each of these slabs, Mr. Ogden passes a horizontal plane. The area of the plane section is, strictly speaking, a circular segment, but is regarded by Mr. Ogden as parabolic. The base and altitude of this parabolic section are determined geometrically by hIr. Ogden and the area of the section taken as ‘/a of their product. The volume of each slab is then determined as the product of this area and the thickness I in. and Vol. B is determined for varying heights as the sum of the volumes of these slabs. This method of calculation is not only inaccurate by reason of the assumption of the section being parabolic, but it is also inaccurate in assuming the volume of each slab to consist of the product of the area of the medial section and the thickness of the slab. As in the case of Vol. A , the magnitude of the latter error is dependent upon the ratio of the “unit of calibration” to the diameter of the tank. ACCURACY-AS stated previously, Mr. Ogden’s method introduces a number of inaccuracies, the magnitude of which is chiefly dependent upon the ratio of the “unit of calibration” to the diameter of the tank. For a given tank of 7 ft. diameter, the error introduced is not very large if the tank is calibrated for each I in. of height. The calculation, however, involved in making this calculation for each I in. of height is very large and consumes a great deal of labor. On the other hand, if the calibration is made for 3 or 4 in. intervals, the labor of calculating is decreased, but errors of considerable magnitude are introduced. It, therefore, becomes a method which requires the sacrifice of accuracy or of simplicity of calculation At the conclusion of hIr. Ogden’s article, he gives an example attempting to compare the true volume of a cylindrical tank and the volume obtained by using his method. This comparison is somewhat misleading. In the first place, it is made between the total volumes of the tank and not between volumes of material partially filling the tank. The errors introduced by Mr. Ogden’s method are by no means a t their maximum percentage value in the case of the calculation of the total volume of the tank. A true index of the accuracy of Mr. Ogden’s method can be obtained only by making the comparison a t the point a t which the errors of Mr. Ogden’s method are a t their maximum percentage value. SIMPLICITY OF CALCULaTION AXD GENERAL APPLICABILITY-
The main criticism of Mr. Ogden’s method does not rest, however, with its inaccuracy, but rather with its lack of simplicity and difficulty of application. As seen from the foregoing description of Mr. Ogden’s method, the determination of the volume content of material in any tank requires a long and laborious calculation of the volume content of each inch of material in the tank, which amounts to a virtual calibration of the tank. Clearly the labor involved in such a calculation which must be made in the case of each tank containing material to be measured, is a feature which argues strongly against this method. I n the past, it has been the custom of engineers to treat these storage tanks as though they were true cylinders. The vertical “innage” of material in the tank is measured and is expressed as a decimal fraction of the diameter. Reference is then made to the engineering tables for “Area of Circular Segments” and a factor is found which corresponds to the above 1
See Kent, “Mecb. Eng. Handbook.” 8th Ed., pp. 121-122.
