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periment resemble closely the distillation for 95 per cent cresylic acid. The presence of the cresols is evident and also the presence of a larger percentage of higher boiling products is indicated by the divergence of the curves in the regions of higher boiling points. The presence of phenols in the straight-run distillates indicates the existence of such materials in crude oil. The very small quantity, however, indicates that the major reaction, producing the phenols, takes place in the cracking still. The similarity of the products produced from petroleum in the cracking still and the products produced by low-temperature carbonization of coal would indicate the same origin of petroleum and coal-namely, vegetation. It is more likely,
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however, that the reaction taking place in a cracking still to produce phenols is dehydrogenation of cyclic hydrogenated hydroxy compounds such as homologs of cyclo hexanol. The quantity of phenols present jn the average cracked distillate is very small, usually less than 0.01 per cent; yet where sanitary conditions demand that they be separated from waste liquors, sufficient volumes may acccumlate to be useful as disinfectants, wood preservatives, or for other purposes for which high-boiling tar acids are suitable. Cracked distillates of sufficiently low-boiling end point may be selected which yield phenol products approximating 95 per cent cresylic acid.
Strength of Curved Walls Exposed to External Pressure' C. A. Andsten E. R. SQUIB% & SONS, BROOKLYN. N. Y.
CANT attention has been paid by the compilers of the standard engineering handbooks to the complex problem of designing spherical and cylindrical walls to withstand pressure applied to their outer surfaces, and it is all too common practice t o build equipment of this kind by guess and by rule of thumb. The estimation of a maximum safe steam pressure for a given jacketed kettle, of a safe thickness of material to be used in constructing a jacket or vessel to withstand a predetermined pressure, and other related problems are often presented to the chemical engineer for solution, but the data in the literature to guide one to a proper solution of such a problem are practically negligible. Although many industrial workers have collected valuable and reliable data, practically none of them have been published, and this secretiveness has forced many builders of equipment to resort to rule-of-thumb methods with consequent waste of labor and material or, what is of greater consequence, the collapse of apparatus used or designed improperly. The thickness of material used is only one of the variables involved in the strength of a spherical or cylindrical vessel exposed to external pressure, and it is the object of this paper to present a graphic method of reducing these variables to a workable minimum. I n this, as in other engineering calculations of the kind, certain assumptions must be made as to workmanship, etc., which have a serious significance in the result that no method of calculation can avoid. The method of calculation here given is based upon the graphic solution of the equations derived by Bach2s3 from a n extensive series of experiments with the actual collapse of the kind of vessels under consideration. By plotting equations derived from those given by Bach, a set of curves is obtained which is of immediate application to design problems.
S
Spherical Shells
To determine the strength of a spherical shell exposed to external pressure, Bach gives the following equations:
1
Received November 2, 1927.
:Z. Vcr. dcct. Ing., 46, 333, 375 (1902).
:"Maschinen Elemente."
K
K K
= 0.3 to 0.4 K O(for cold-worked copper) = 0.25 to 0.35 K , , (for wrought iron)
=E,
2sK orp = -
(2b)
(3) where K O = tension in kg. per sq. cm. a t which wall will collapse K = safe tension in kg. per sq. cm. A and B = empirical constants based on material used p = pressure in absolute atmospheres r = radius of curvature of the spherical surface, in cm. s = thickness of wall, in cm.
The values of the constants A and B as determined by Bach for different materials are as follows: For cold-worked copper, A = 2550 and B = 120 For wrought iron, A = 2600 and B = 118
As an example of the application of these formulas, let us assume that one is to determine the safe pressure to be applied to a spherical shell of cold-worked copper having a radius of 41.1 cm. and a thickness of 0.57 cm., and in other respects properly built. Substituting in (l), K O = 2850 - 120d\/72.1 = 1531 kg. per sq. cm. K = 0.3 X 1531 = 459.3
Substituting in (3),
='
0'57 459'3 41.1
=
12.73 absolute atmospheres
I n applying these formulas to design, one must assume that: (1) the material and workmanship will be first class; (2) the ratio of the radius of the spherical surface and the diameter of its plane face (d = 2a) has been properly selected (see below); (3) no temperature differences exist in different parts of the wall; (4)temperatures used will not seriously affect the tensile strength of the material used; and ( 5 ) no undue strains are set up in fabricating the material. I n good design, the ratio r/2a (2a being the inside diameter of the vessel) should be selected so that 0 . 5 5 ~to 0 . 6 5 ~is equal to the height, h, of the spherical segment. The relation between the radius of curvature of the sphere, the diameter of the segment, and its height are given by the following equation: a2
A
r = s + z
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365
revaluation of the constants. It is probable that the curve for pure aluminum would run under the copper curve and a t about the same distance from it as the iron curve, provided the aluminum is used within the proper temperature range to give it the tensile strength required by the values of the constants used. It is thus possible, having calculated the wall thickness of a known material, to approximate more or less closely that required of an unknown material to perform the same service by a comparison of the respective tensile strengths of the two
/4
Fiqure I
Cylindrical Vessels
Bach gives the following formula for the determination of the resistance of cylindrical vessels to external pressure, and Melhardt4 has found it quite satisfactory from an engineering point of view, although it does not strictly hold in all cases:
-)1
f
c
P I+d In this equation, k , a, and c are constants evaluated more or less empirically, s = thickness of wall in cm., p = pressure in absolute atmospheres, I = length of tank in em., and d = diameter of tank in cm. The constant k is derived from the tensile strength of the metal, expressed in kilograms per square centimeter, by applying an empirical factor of safety. For wrought iron the value of this constant is 600 kg. per sq. cm. (8250 lbs. per sq. in.), the factor used being about 5.5. For copper, k = 400, and for aluminum, k = 200. In selecting the value of the factor employed in determining this constant, it must be borne in mind that tensile strength of materials frequently 4k
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derived from consideration of similar triangles. By applying our empirical rules, we find the best proportions to be r = 1.02 to 1.16~. The Bach formulas given above do not hold for values which made r greater than 167s, as under such conditions the effect of the curvature of the metal is greatly changed. I n a spherical vessel the effect of the thickness of the material in forming an arch must be taken into account in determining its strength in resisting pressure applied externally, and since this effect is dependent upon the relation of thickness to the radius of curvature of the surface, the limitation of this ratio must be considered in design. The formulas given are purely empirical and this assumption has been made in reaching them. To bring the foregoing equations into usable form for graphic interpretation, we may eliminate the KO and K terms and reach the following equations:
$
- 0.6B. -
0.3 ( A - B $ )
= $orp
and p = 0 . 5 A . 2
- 0.5B. :-$, for wrought iron
= 0.6A.:
-,forcopper;
By substituting the proper values of A and B given above in these two equations and plotting the values of p against r/s, the curves for copper and iron vessels shown in Figure 1 are obtained. The application of these curves is a simple matter. If it is desired to find the proper ratio of r to s to withstand a given pressure or the pressure safely to be used in a vessel having a given ratio of r to s, these values may be read directly from the curves given. Having thus reached the evaluation of these ratios, the application of the empirical rules given above will enable one easily to determine the required values. The application of these equations to problems involving metals other than iron and copper would require the determination of the proper values of A and B for the other metals, but in general the curves would follow the same shape, being merely displaced to the extent required by the
shows sharp breaks with changes of temperature and the values used must therefore take into account the temperature of operation. The constant a depends upon several important factors, such as workmanship and the position of the tank in use. For ideal conditions its value is 0. The following values may properly be assigned to it for particular conditions: (1) Longitudinal seam-welded or butt-welded with riveted double-strap butt joint For vertical cylinders, a = 50 For horizontal cylinders, a = 80 4
Chem. A p p . , 14, 169 (1927).
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366
OOCLI
( 2 ) Longitudinal seam riveted lap joint For vertical cylinders, a = 70 For horizontal cylinders, a = 100
The constant c is intended to thicken the material to care for losses due to corrosion, erosion, and similar factors, In common boiling kettles Bach gives c the value 0. HausbrandJ5using the same values for k for iron and copper in this equation, makes up the differences between the two metals by varying the value of c. Thus he gives c, for iron, a value of 2.0, and for copper of 0.2 (6-s), and in calculating on this basis gets thicknesses for iron greater than for copper to withstand the same pressures. Obviously, this renders the values given in his book inaccurate for general use. Assuming values for ratio of length to diameter, l / d , and for the constant, n, curves may be plotted for pressure against 6
“Hilfsbuch fur den Apparatenbau.”
A Clamp for Rubber Tubing’ Harold W. Batchelor 0x10 AGRICULTURAL EXPSRIMSNT STATION,WOOSTSR,OHIO
H E following method of clamping rubber tubing to glass tubing for general laboratory apparatus or for pressure or vacuum systems has been found very satisfactory. A sleeve, c, approximately 11/2 inches (3.8 cm.) long may be made of thin glass tubing whose inside diameter is but slightly larger than the outside diameter of the tubing to be used. The sleeve is first slipped several inches on the rubber tubing. The tubing is then slipped into place on the glass tubing, a. While holding both the glass and the rubber tubing at b, the latter is stretched slightly so that it assumes the position indicated by the dotted lines a t d. The glass sleeve is then put in position and the rubber tubing worked back into position as shown by the heavy lines a t d. When the rubber tubing has been properly worked into position, the clamp is so effective that it is practioally impossible to remove the tubing when pulling a t b. By stretching the tubing again a t d and removing the sleeve, the two tubes can be easily separated again. Though not usually 1
Received February 9, 1928.
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the ratio of thickness to diameter, s/d. The accompanying Figures 2, 3, and 4 give values for copper tanks on the supposition that c = 0. The designer should bear this in mind in adapting these curves for use under conditions which will require greater wall thicknesses than those calculated. I n using these curves for aluminum work the value obtained from the curve for the required condition is multiplied by 2.0. For iron the value obtained is divided by 1.5. The curves may be similarly adapted to use with other metals by making proper allowances for differences in tensile strength. In designing a cylindrical tank, the practical minimum of labor and materiale is attained when I = ?T d. I n general, vessels having a ratio of length to diameter between 1 and 4 are most economical to design and build from all practical points of view. 6
Chem. Met. Eng., 84, 379 (1927).
necessary, the clamping effect may be increased by slightly widening the end of the glass tubing a t e. If the clamp is used in the construction of gas-analysis apparatus, a mercury seal would scarcely be necessary, since the rubber tube is clamped uniformly throughout its circumference. The clamp may be modified, horvever, to form a cup for a mercury seal as shown a t f. A mercury seal to connect two rubber tubes can be easily prepared by welding a side arm a t the midpoint of the sleeve. Such a cup can be used either with a straight side arm in a horizontal position or in a vertical position with the side arm bent to a vertical position. The sleeve also affords an e x c e l l e n t protection for the rubber tubing if it is necessary to wire it in position on a base as shown. It is hoped to make available in the near future either metal or other tubes for this purpose.
