ANALYTICAL EDITION
July 15, 1942
In use, the viscometer is filled approximately t o mark J. When the liquid has attained operating temperature, the level is depressed from J t o F, the excess overflowing at C . To start a viscosity determination, the liquid level is depressed t o a point a little below mark H . The efflux time is that elapsing during the passing of the meniscus between points H and G under the sole influence of gravity. Since the body of the liquid advances over the marks, there is no difficulty in the measurement of the efflux time even when its color is very dark. This instrument is suitable for use with residual oils, the less viscous solvent extracts, and similar materials; however, it is not designed for highly viscous materials of any type. Perhaps 2000 centistokes would represent the maximum practically measurable viscosity. Acknowledgment
The author Wishes to express his appreciation to R' "Iutt for his continued interest during the course of this work.
595
Grateful acknowledgment is made to the Battelle Memorial Institute for permission to publish this material. Literature Cited (1) Cannon, M. R., and Fenske, M. R., IND.ENQ.CHEM., ANAL.ED., 10, 297 (1938). (2) Dean, E. W., Bauer, A. D., and Berglund, J. H., IND.ENQ.CHEM., 32, 102 (1940). (3) FitzSimons, O.,IND.ENQ.CHEM.,ANAL.ED., 7, 345 (1935). (4) Ruh, E . L., Walker, R. W., and Dean, E. W., Ibid., 13, 346 (1941). (5) Ubbelohde, L.,Ibid., 9, 85 (1937). (6) Zeitfuchs, E.H., Natl. Petroleum News, 31, 262 (1939). (7) Zeitfuchs, E. H.,Proc. 0th Mid-Year Meeting Am. Petroleum Inst., Sec. III, Refining, 20, 104 (1939). PrmsmmED before the Division of Petroleum Chemistry a t the 102nd >feeting of the ~ M E R I C A NCHEZllIClL SOCIETY, Atlantic City, N. J.
An Electromagnetic Densitometer A. R. RICHARDS, Trinidad Leaseholds, Ltd., Pointe-&-Pierre,Trinidad, B. W. I.
A n apparatus is described in which the principle of balancing the attraction of a magnetic field against the upthrust on a submerged armature is used as a rapid method of measuring liquid densities. The precision of the determinations depends on the range of the instrument and is of the order of 1 part in 800 for densities between 0.62 and 0.82 gram per ml.
Now ( V N - V , ) / A s mAs = M = VI where moment, volume, and armature, respectikely.
H , the strength of the field, and M , v, and I repreqent the magnetic intensity of magnetization of the Thus
=
E = vIH
The work done during a small displacement, ds, of the armature is given by the equation which follows :
C
ONSTRUCTION of the densitometer described below was undertaken in order to facilitate density determinations on some two hundred 5-mi. samples every 8 hours. Ordinary hydrometers were unsuitable, since they require a t least 20 ml. of sample, while pycnometer measurements would have been too slow. The essential parts of the instrument consist of a small glass float held under the surface of the sample by a n adjustable stop and a small coil surrounding the lower portion of the sample tube. If current passing through the coil is gradually increased, the resulting magnetic field will eventually exceed a critical value, such that the force on the armature will become sufficient to draw the float away from the stop. If suitable precautions are taken, the density of the sample may be determined accurately by measurement of the critical current. Theory The theoretical considerations affecting the design of the apparatus can be expressed in the following manner: Let the pole strength induced in the armature be m and the magnetic potential a t these poles be V N and V,. It follows that the potential energy, E, of the armature in the field is given by:
where As is the distance between the poles.
FIGDRB1. DIAQRAM OF APPARATUS
Vol. 14, No. I
INDUSTRIAL AND ENGINEERING CHEMISTRY
596
Fds = od(IH)
where F is the force acting on the armature along the direction of displacement. Then F = - vd(IH) ds
The relation between I and H depends on the susceptibility,
k, and the geometrical form of the armature. For small values of H, k may be regarded as constant and in general, I = Hf(k) and
A water jacket completely surrounding the float chamber is used for maintaining a standard temperature during determinations. Drift due to rise in temperature of the coil is not noticeable with currents below 600 milliammeters and the insertion of a water jacket between the drain tube and the coil is not necessary. It is easy t o maintain a temperature constant to within *0.2’ C. which produces an error of less than 0.0002 gram per ml. in the densities of gasoline fractions. The instrument can be reset after cleaning by adjusting the position of the stop until the milliammeter reading for a liquid of known density agrees with the original calibration. This setting is checked by the use of a second liquid.
By analysis of the experimental figures given in Table I, it can be shown for this instrument that d::c.
Now H = i#(s) where i is the current flowing in the coil producing the field, and #(s) is a function determined by the configuration of the system. Therefore,
Hence F = Biz *(s)
Since the float always starts from the same position, t h e value of \k(s) has a fixed value for any given position of the stop. Hence, F = Cis where C is a constant. If the volume of the float is V and the density of the liquid is p, the upthrust on the totally immersed float is p V . When the current in the coil reaches the critical value the opposing W , where W is the weight of the float force is F p v = ci2
+
=
0.701 iz
+ 0.621
(1)
TABLE I. DENSITY MEASUREMENTS Current,
d?&, from
d?&. from
Amperes 0.085 0.152 0.179 0.223 0.302 0.383 0.397 0.424 0.425 0,445 0.459 0.475 0.477 0.488
Pycnometer 0.6255 0.6370 0.6429 0.6563 0.6842 0.7230 0.7309 0.7445 0.7458 0,7598 0.7673 0.7795 0.7811 0.7874 0.7962 0,7974 0.8082 0.8146
Equation 1 0.626 0 637 0.643 0.656 0.684 0.723 0.732 0.746 0.747 0.759 0.788 0.778 0.780 0.788 0.797 0.798 0.807 0.813
0.500 0.502 0.515 0.521
Difference Calcd. and
Found
+o.ooo +o.ooo +o.ooo -0.000 -0.000 -0.000 +0.001 +0.001 +0.001 -0.000
+0.000 -0.001
-0.001 +0.000 f0.000 f0.000
-0.001 -0.ou1
+w
or p =
Ri2
+P
where R is constant, providing the geometrical arrangement of the apparatus is reproducible, and P is the density of the float. I n order to prevent permanent magnetization of the armature and minimize sticking of the float, alternating current from a step-down transformer is used in the field coil. The value of i in the above equation is in practice, therefore, the value recorded by an alternating current milliammeter. A Westinghouse Type PY5 has been found suitable in this service. The sensitivity of the densitometer is increased and the range decreased by increasing the size of the float, reducing the size of the armature, and reducing the number of turns in the field coil. Since the float is submerged, surface tension effects are eliminated.
Experimental The detailed design of the apparatus is shown in Figure 1. The float, A , constructed from Pyrex glass, encloses an armature made from a short length of iron nail. The mean density of t h e float is adjusted by adding or removing glass at the tip until it just floats in liquid, the density of which corresponds t o the lowest value of the range required. The inside diameter of the float tube should be about 2 mm. greater than that of the float to ensure a free passage without unduly increasing the volume of the apparatus. The float is centered on the bottom of the stop. The lower end of the float tube is sloped to allow easy drainage and the drain tube allows 0.5-mm. clearance around the tail of the float. The three-way tap is sealed on after mounting the coil; the lower limb is used as a drain and the side limb serves t o admit air for drying the apparatus. The bearing for the adjustable stop is cemented in place after insertion of the float. The coil is wound on an ebonite former with a thin core and consists of about 28 grams (1 ounce) of double cotton-covered copper wire 23 A. W. G. It is connected in series with a 20-volt alternating current transformer and the variable resistance assembly shown. This circuit gives the most satisfactory control.
Although the range of measurement can be adjusted, i t is not convenient to construct a n instrument with a range of more than 0.2 gram per ml., since the precision is limited by the accuracy with which the milliammeter may be read, which is of the order of * 1ma. over the 750-ma. range. Substituting the value of this uncertainty, 6i, in the following equation d&
* 6d
=
0.701 (i * 6i)*
+ 0.621
gives the maximum uncertainty in the density, 6d, as *0.0007 gram per ml. for currents not in excess of 500 ma. A similar error arises during calibration, so that the maximum error is not more than *0.0014 gram per ml. If the instrument has been cleaned and reset but not recalibrated, a further additional error of not more than *0.0007 gram per ml. must be included, making the greatest uncertainty under the least favorable conditions not more than *0.0021 gram per ml. or 1.0 per cent of the useful range. The difference between t.he observed and calculated densities shown in Table I exceeds in certain cases the estimated precision for given current values. This is due to absolute errors in the milliammeter, since i t is stated by the makers that the values indicated may differ from the absolute values by 0.5 per cent of the full-scale readings of both the 250- and 750-ma. ranges. I n view of the above, i t is recommended that densities be read from a n experimental curve determined for a given instrument and milliammeter and covering the entire range. Since the sensitivity can be increased a t the expense of the range, the ultimate precision is limited only by temperature control and the reproducibility of the initial system.
Acknowledgment The apparatus was developed in the laboratories of Trinidad Leaseholds, Limited, to which company thanks are due for permission to publish this paper.
