KC. Hayes S. Q.W Lewis. Measuremeot of viscosity / ■•V siifsp; ■ f ' ’■■ "•■■ - ;'2i-''iv.' ■ ■ "' ■■> :•• Av; ‘V’ :*'► :i ' 'AA . .- •♦i 1 ■'», •■'•.■^'^ 1 ^ I ' <>■> ,;■ ’■•IftH , ;;%* (.v«> ■» -> A- .,>.>A ; ' V*. j. • ■ ^ “ ■\Av,',f,:.. ■■ ■■ 'iw 4 '^: 3 ' ■••'" '' 'aO'^ iUtU ^ i ■< ' A ' ' f.ifjrtl; , ' i'. • ■' . ■: .kiA I ‘ ' .‘ /r-i • ■ 'Jjjfev ; .:'v ■ •-:■'■'■ '-V^' • ' .., 'A A li-. hJ A.A A , ',, ■ 1 V '>-v THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 29 WEST THIRTY-NINTH STREET, NEW YORK THE MEASUREMENT OF VISCOSITY AND A NEW FORM OF VISCOSIMETER BY H, C. HAYES AND G. W. LEWIS To be presented at the Spring Meeting of The American Society of Mechanical Engineers, New Orleans, La., April 11 to 14, 1916. THE MEASUREMENT OF VISCOSITY AND A NEW FORM OF VISCOSIMETER By H. C. Hayes and G. W. Lewis ABSTRACT OF PAPER This paper deals with the measurement of viscosity. It predicts the errors which are introduced by the various types of viscosimeters and verifies these pre- dictions in case of the short capillary types such as the Saybolt, Engler, and Redwood and the orifice types such as the Carpenter, by comparing the temper- ature vs. viscosity curve for a light and a medium lubricating oil, as given by. these meters, with the true curves as determined by a modified form of Poiseuille’s capillary tube method. The work shows that the short capillary types give results about 50 per cent too small and the orifice types give results about 100 per cent too small, and further, that none of these meters give accurate comparative results for two dif- ferent oils or for the same oil at different temperatures. The only type of viscosimeter on the market that can be expected to give accurate results on theoretical grounds is the Stormer. This instrument at- tempts to measure the viscosity in terms of the torque required to spin a disk within the liquid, but the mechanical difficulties met with are such as to debar this type. The authors have designed and thoroughly tested out a viscosimeter which embodies all the good points of the Stormer and none of its defects. They measure the viscosity in terms of the torque which a cylinder experiences when suspended within a rotating liquid. This method eliminates all error due to friction. The results given by this meter agree with the true curves for the light and medium oils to within 1 per cent and can safely be used as a standard. The advantages of this viscosimeter are evident. The instrument can be calibrated to give direct readings of the viscosity; the oil is not handled during a complete test at various temperatures; the design of the instrument is such that the temperature of the specimen follows closely the temperature of the bath, so the data for the temperature vs. viscosity curve can be taken while the sample is cooling; the meter gives the viscosity of mixtures, such as paints, as well as for liquids that have been carefully filtered; there are no glass parts to break; the personal error is eliminated and the meter can be made self recording. 1 THE MEASUREMENT OF VISCOSITY AND A NEW FORM OF VISCOSIMETER By H. C. Hayes,^ Swarthmore, Pa. - and G. W. Lewis, 2 Swarthmore, Pa. Non-members In determining the lubricating properties of an oil, the viscosity - test is considered of great value, since by means of this test a good oil can readily be distinguished from a poor one. It is therefore very important that the engineer be able to measure the viscosity of an oil and also the variation of viscosity with temperature. *2 The present paper, dealing with the measurement of viscosity, gives in part the results of a somewhat extended research on the lubricating properties of oils. It is to be followed by a paper giving the relation between the lubricating properties of oils and various easily measurable physical properties. VISCOSITY 3 Matter in all states exhibits a gradual yielding to tangential forces which tend to change its form. This property is termed viscosity and may be defined quantitatively as the tangential force per unit area divided by the shear per unit time. 4 To gain a clear physical concept of this definition, consider a plane surface. Fig. 1, of area>S, parallel to and at a distance d from another large plane surface, and the intervening space filled with a liquid whose coefficient of viscosity is rj. If a given force, F, acting on this plane, is applied to S, the surface will be dragged along and ^ Prof, of Physics, Swarthmore College. 2 Asst. Prof, of Engrg., Swarthmore College. For presentation at the Spring Meeting, New Orleans, La., April, 1916, of The American Society of Mechanical Engineers, 29 West 39th Street, New York. All papers are subject to revision. 3 >01072 4 MEASUREMENT OF VISCOSITY will finally attain a steady velocity, which denote by V. In accord- ance with the above definition, the relation between these various factors would then be r, = F/S V/d or n = F .d-^ S-V W the value of v depending on the units in which these various factors are measured. If absolute values are desired, the factors on the right hand side of the equation are to be measured in C.G.S. units, but if relative values will suffice, as is the case in nearly all engineering work, they may be measured in any units. 5 It must be borne in mind that equation [1] is not true w en the velocity, V, is changing, for then only a part of the force, F is used to overcome viscosity, a part being used in giving acce era e Fig. 1 Conception of Viscosity motion. Under such conditions, another term “ust be added to this equation. The nature of this term is not difficult to see, for !et equation [1] be written F= v-S-V/d. When there is ac- celerated motion, the force, F, will be divided into two Pa^s, the part used to overcome viscosity and that used to give acce motion Call these parts /i and respectively, then at any instant Z T+ f. where /= , • S • F/d and /. = M • dV/dt, where M is the mass that is being accelerated and dV/dt is the average change of velocity per second of this mass. The complete instantaneous equation thus becomes F = V SV/d + M • dV/dt and the viscosity cannot be found from this equation unless the last term can be evaluated, which is usually difficult and often impossible. development of a working formula 6 In most physical measurements, comparative values are more easily obtained than absolute values. As a result measurements aie rnTde Tterms of some standard, the absolute value of which h^ been determined by a more or less laborious proce®. In K measurements of viscosity, the standard usually chosen is water a temperature of 20 deg. cent. H. C. HAYES AND G. W. LEWIS 5 7 Girard and Poiseuille, by studying the flow of liquids through capillary tubes, were the first to measure the absolute value of viscosity vdth anything like accuracy. On the basis of his excellent experimental work on the viscosity of water, Poiseuille deduced the formula V = H/L where V = volume of liquid transpired L = length of capillary D = diameter of capillary H = pressure K = constant for each liquid at a given temperature. Later, this empirical formula and its corrections were proved by several investigators.’^ 8 By assuming there is no slip at the surface of the capillary, that the liquid flows steadily without eddies or turbulent motion, and that there is no kinetic energy of efflux, then the trans- piration formula for a liquid flowing under its own head becomes ‘ ^7 = I Qigr^/lv) pi where ri = coefficient of viscosity (often contracted to viscosity) h = liquid head g = acceleration of gravity r = radius of capillary I = length of capillary V = volume of flow t = time of flow p = density of liquid. Experiment shows that the first assumption is true if the liquid is one that wets the surface of the capillary. The work of Reynolds shows the second assumption is true if the velocity of the liquid through the capillary is kept less than 700 • ? 7 /p • r cm. per sec. The third assumption, of course, can never be true. The liquid ^ Stokes, Trans. Camb. Phil. Soc., 1849, vol. 8, p. 287; Wiedmann, Pog- gendorf^s Annalen, vol. 99, p. 177; Hagenback, Pogg. Ann., vol. 109, p. 385; Stefan, Wien. Bar., vol. 46, p. 495; Couette, Ann. Chim. Phys., vol. 21, p. 433; Neumann, Vortrage iiber Hydrodynamik; Wilberforce, Phil. Mag., vol. 31, p. 407; Jacobson, Arch. f. Anat. u. Physiol. 1860, p. 80; Knibbs, J. Roy. Soc. N.S.W., vol. 29, p. 77; Boussinesq, Compt. Rend., vol. 110, p. 1160; Brillouin, La Vis- cosity (Gauthier Villars, 1907). 6 MEASUREMENT OF VISCOSITY must have kinetic energy when it leaves the capillary-. In accord- ance with equation [2], a correction term must be added which, ac- cording to Couette, Finkener, and Wilberforce, should be -vp/Sirlt, The complete expression for the viscosity is therefore of the form n =p (A.t-B/t) where A and B are constants for any piece of apparatus, p and t are the density and time of flow, respectively. 9 After a thorough examination of the recorded data on the viscosity of water, Knibbs concluded that the correct formula should be ^ = Trhgr'^pt/Slv — lA2vp/STrlt It is to be noted that the correction term is larger than that given by Couette. Moreover, this correction term varies with the time of flow approaching zero when the velocity of flow is very slow, in which case t becomes very gi'eat. The value of the term increases with the temperature of the liquid since the time of flow decreases, and so the percentage of error in a viscosity vs. temperature curve due to neglecting this correction factor will increase abnormally toward the higher temperatures. This is due to two causes, the correction to be applied increases with the temperature and the value of the quantity to be corrected decreases rapidly with the temperature. Attention will be called to this fact when some of the various com- parative methods are discussed. It is further to be noted that this correction term varies inversely as the length of the capillary. A short capillary requires a large correction term. 10 This formula, as corrected by Knibbs has been submitted to careful experimental test by Hosking, and by Bingham and White. These investigators have determined the constants of the formula experimentally and have obtained fair agreement with theory. The capillary tube method, as employed by these experi- menters, though complicated and laborious, can be depended upon for giving absolute values of the viscosity, and the accuracy of any viscosimeter can be determined by a comparison with the results obtained by this method. CLASSIFICATION OF VISCOSIMETERS 11 Class 1. Short Capillary. In meters of this type, the liquid to be tested is forced either by gravity or by pressure through tlie capillary and the viscosity is determined in terms of the time re- H. C. HAYES AND G. W. LEWIS 7 quired for a given volume to pass through the meter, as compared with the time required for a standard liquid to discharge the same volume. 12 A cross section of a meter of this type is shown in Fig. 2. The essential parts of the instrument are a cylindrical bowl, A, in which the oil is placed and a short capillary tube B, through which it is discharged. The instrument must have temperature controlling and measuring devices, means for starting and stopping the flow and volume and time measuring apparatus. 13 To this class belong the Saybolt meter, adopted as a standard by the Standard Oil Co.; the Engler meter, adopted as a standard by the U. S. Government and Germany; the Redwood meter. Fig. 2 Short Capillary Type Viscosimeter adopted as a standard in England ; the Scott meter ; and the pipette, adopted as a standard by the Pennsylvania Railroad and much used by chemists. The majority of the viscosimeters on the market are of the short capillary type. 14 Class 2. Orifice. This type employs an orifice in place of the short capillary of the previous type. Fig. 3 is a section of such a meter, in the cylindrical bowl. A, of which the oil to be tested is kept at constant head above the orifice, B. The Carpenter meter belongs to this class. 15 Class 3. Dropping a solid body through a luhe filled with the liquid, the solid body being usually a sphere or a plunger. Meters emplojdng this principle determine the viscosity in terms of the 8 MEASUREMENT OF VISCOSITY time required for the body to drop a certain distance through the liquid, as compared with the time required for the same body to drop through a standard liquid. To this class of meters belong the Perkins meter which employs a plunger and vertical tube, and the Fig. 3 Orifice Type Viscosimeter Flowers meter ^which employs a small steel sphere and a slanting- tube. |i 16 Class 4. Oscillating Disk or Cylinder. These meters de- termine the viscosity in terms of the damping which the oscillating disk or cylinder experiences when placed in the liquid as compared with the damping when placed in the standard liquid. The Doo- little meter is an example of this class. H. C. HAYES AND G. W. LEWIS 9 17 Class 5. Rotating Disk or Cylinder. This type determines the viscosity in terms of the speed of rotation of the disk or cylinder in the liquid under test as compared with the speed of rotation in the standard, the driving torque remaining constant. The Stormer meter is an example of this class. DISCUSSION OF THE VAKIOUS TYPES 18 The value of each of the above types, so far as accuracy is concerned, can be estimated by noting whether they operate in ac- cordance Avith equation [1] or [2], but before speaking of the various types it should be noted that only equation [1] will give accurate comparative results. 19 Write this equation in the forms yfx ~ F X * dx/ F>x • T X where the subscript x refers to the substance and conditions met with in connection with the liquid to be tested, and Vs= Fs-dJS,.\\ where the subscript s refers in a similar manner to the standard liquid. Solving these two equations for y gives rix = Vs • S,.V,-Fx- dx/F, . d , . .S, . TT an expression which simplifies to = r;, (Fx/F,) if the same apparatus is used in both cases, whereas if we apply the same operation to equation [2] we get V. = Vs [Fx - . dVx/dtx)/{F, - M , . dVJdQ] VJVx 20 This expression cannot be simplified, for the expression within the brackets can never be made equal to unity. Moreover this expression is not constant, but varies with every liquid which is compared with the standard and with every change of temperature. It is therefore impossible to assign an accurate correction factor to an instrument which seeks comparative results if the instrument operates in accordance with equation [2], or, in other words, if there is any accelerated motion of the liquid during the testing operation. 21 In practice, the time, t, required for a definite volume of liquid to pass through the meter is measured instead of the velocity, V, and, if the force driving the liquid is gravity, the force F is easily 10 MEASUREMENT OF VISCOSITY evaluated as p • A, where p is the density and./i the average head. Equations [ 1 ] and [ 2 ], in practice, thus become Vx= Vs-ix-t,. h/t, • p,-h or - = [la] Vx = Vs - tx/t,[px • Ti - (M ^ . dVx/dQ/(p, .h - M,- dVJdQ]. [2a] THE ACCELERATION ERROR 22 It is obvious that equation [2a] applies to all meters coming under Classes 1 and 2 since the liquid starts from rest in the meter chamber and leaves with a certain velocity and must therefore experience acceleration. In all these meters on the market the ac- celeration term (M • dV I dt) is neglected since its evaluation is im- possible and the formula then becomes identical with equation [la]. An error which we shall call the acceleration error is thereby intro- duced. 23 The nature of this error can be predicted from an inspection of equation [2a]. The liquid having the smaller viscosity will pass through the meter with the greater velocity and the correction term (M . dV I di) will be larger in proportion for this than for the more viscous liquid. If, therefore, water is chosen as a standard in de- termining the viscosity of lubricating oil or any liquid which is more viscous than itself, the value [(E — M • dV/dt)/{F — M • dV /di)] will be larger than the value F /F and the value r? as computed from the approximate formula [la] will be too small. If, however, the liquid under test has a smaller viscosity than the standard the bracketed term will have a smaller value than F /F and the result as given by the approximate formula will be too large. 24 In the case of meters employing capillary flow, it is evident that the acceleration term will increase with the diameter of the capillary and decrease with its length and, as a result, we shall expect all meters using short capillaries to be subject to large error. More- over, if we regard the orifice as a very short capillary, we should expect the error introduced in this type of meter to be still greater. The experimental results presented later prove these predictions to be correct. SURFACE TENSION ERROR 25 Another error introduced in all the flow type viscosim- eters, of both the capillary and orifice forms, is due to difference in the surface tension of the standard liquid and the liquid under H. C. HAYES AND G. W, LEWIS 11 test. This error is prominent for those meters which discharge from the capillary or orifice into the air. As soon as the stream leaves the meter the film which forms on the free surface tends to contract, and thus decreases the cross section of the stream and retards the dis- charge. This contraction is greater for a liquid of high than for one of low surface tension. If water is used as the standard, since its surface tension is greater than for oils the flow of water will be re- tarded more than the flow for oils. The time of flow, will be in- creased in greater proportion than tx, thus giving the ratio tx/ts, too small and the error will cause the value to be too small. For oils and most liquids, the surface tension error and the acceleration error are additive. 26 This surface tension effect is, of course, negligible for a stream having high velocity, as the inertia of the moving mass prevents dis- tortion of the stream lines. For the low velocities of efflux given by flow type viscosimeters, however, the effect is very noticeable, as can be seen by measuring the diameter of the efflux for two liquids of different surface tension. When conditions are most favorable for reducing the acceleration, namely velocity of efflux very small, they are most favorable for introducing the surface tension error. CKITICAL VELOCITY ERROR 27 Another source of error in most capillary and orifice forms of viscosimeters is that the dimensions of the instrument are such that for the standard — water — the flow exceeds the critical velocity and the resulting turbulent flow makes the value of t abnormally large. This introduces an error, which also adds itself to the ac- celeration and surface tension errors. This fact was discovered during the research work about to be recorded but has, in the mean- time been noted and investigated by Upton who found the error so introduced by the Engler viscosimeter to be great. 28 The three errors — acceleration, surface tension and critical velocity — are prominent in all the meters named above as standards and we should expect the viscosity as given by these meters to be in general much too low. The experimental results will show that it is. 29 Those meters based on the principle of dropping a solid body through a tube filled with the liquid to be tested should be more accurate than the capillary or orifice forms as they are free from the surface tension error and usually from the critical velocity 12 MEASUREMENT OF VISCOSITY error. All are, however, subject to the acceleration error. All the liquid displaced by the falling body suffers acceleration. These meters are all of the flow type and may be regarded as of the short capillary form, the reduced section at the point where the falling body is passing being the capillary. The liquid flows across this section as truly as it does through the orifice or capillary. 30 The relation between the damping which an oscillating disk or cylinder experiences and the viscosity of the liquid in which it is immersed is complicated, and indeed the true relation is not known. Meters based on this principle, such as the Doolittle meter, do not give accurate results. They are nearly free from the surface tension and critical velocitv errors, however, and though somewhat slow and difficult to operate, they give better results than the majority of flow types. 31 The constant speed of rotation which a disk or cylinder immersed in a liquid will attain under the action of a constant torque is a true measure of the viscosity of the liquid. The Stormer viscos- imeter attempts to operate in accordance with this principle, but the friction of the moving parts is necessarily such that a constant torque cannot be obtained. With proper refinement, this meter could be made to give good results. The fact that a meter based on this principle can theoretically give accurate results has led to the development of a new viscosimeter now to be described. THE NEW VISCOSIMETER 32 This viscosimeter operates in accordance with the principle that a solid body having a surface of revolution experiences, when suspended in a rotating liquid, a torque which is proportional to the viscosity of the liquid. The instrument is shown diagramatically in Fig. 4. The specimen, S, is contained within a cylindrical chamber Tvhich is caused to rotate uniformly by a motor, M, through a worm drive, R. A cylinder, C, is suspended within the specimen by a thin steel wire, W, so that the axis of the rotating liquid coincides with the axis of the cylinder. The specimen chamber is provided with- a cap, V, so shaped that the excess liquid can overflow when the cap is seated and thus give constant conditions within the chamber. The specimen chamber is surrounded by an oil jacket, J, in which a thermometer, T, is suspended. The jacket oil may be brought to any desired temperature by means of a heating coil, or a side coil not shown in the diagram. The cover, P, of the jacket chamber H. C. HAYES AND G. W. LEWIS 13 is provided with a scale which is marked in degrees or may be cali- brated to read off directly, through the deflection of the pointer, P, the viscosity in terms of a standard liquid. The specimen chamber and the suspended cylinder are both made of copper to insure con- stant temperature throughout the specimen and the outside of the specimen chamber is provided with blades which keep the jacket oil thoroughly mixed as the chamber revolves and thereby exposes the latter to a uniform temperature. This is an important factor toward insuring constant temperature throughout the specimen. 33 The experimental work has shown that the temperature of the specimen is uniform to within a small fraction of a degree. More- over, the temperature of the specimen follows the temperature of the jacket oil so closely that the temperature-viscosity curve can be taken while the temperature is slowly raised or lowered. This 14 MEASUREMENT OF VISCOSITY proves to be a great saving of time. It also saves labor, for one does not need to stand by the instrument continually. The de- flection of the pointer is at any instant a measure of the viscosity, so all that is required is to take simultaneous readings of temperature and deflection at intervals during the heating or cooling process. EXPERIMENTAL RESULTS 34 To test the accuracy of this viscosimeter, the temperature- viscosity curve was found for a light and a medium gas engine oil by the capillary tube method, the apparatus for which is shown in Fig. 5. The oil was drawn from vessel A to vessel B, and vice versa, by connecting each in turn with the partial vacuum chamber, C. These vessels were submerged in a thermostat which could be main- tained at any desired temperature. The results, in terms of the viscosity of water at 20 deg. cent., are given by the points enclosed in circles for curves 1 and la. Figs. 6 and 7, the latter referring to the lighter oil. The viscosity of these same oils as given by the new meter is represented on curves 1 and la by the points enclosed in squares. The agreement between the two methods is almost perfect. 35 The viscosity of these oils as given by a meter of the short capillary type. Fig. 2, is given in curves 2 and 2a. Curves 3 and 3a give the viscosity of these oils as obtained with a meter of the orifice form. Fig. 3. As predicted, the results given by the short capillary V'iCO&ifi) Viscosi+y n. C. HAYES AND G. W. LEWIS 15 Temperature, Dey. Fa hr. Fig. 6 Viscosity Curves for Medium Gas Engine Oil Fig. 7 Viscosity Curves for Light Gas Engine Oil 16 MEASUREMENT OF VISCOSITY type are much too low (on the oils tested about 100 per cent too low) and the results given by the orifice type are still lower. CONCLUSIONS 36 The errors inherent in all flow types of viscosimeters have been predicted and the predictions verified by experiment. The magnitude of the errors are such that these meters cannot be de- pended on for giving even approximate results. The various meters of this type on the market do not give results which are in agree- ment, and no one of these meters can justly be claimed as a standard. 37 The new viscosimeter of the non-flow type described has the following advantages: 1 It gives values for the viscosity which are in agreement with those given by the standard capillary tube method. 2 During a series of tests at various temperatures, the oil is not handled. 3 The sensitiveness of the instrument can be made any- thing desired by changing the speed of rotation of the specimen or by using suspension wires of various diam- eters. 4 The density or change in density is not a factor in com- puting the results, in fact the instrument may be gradu- ated to read off the viscosity directly. 5 The viscosity of liquids which contain particles in sus- pension can be measured, and the operation of the meter is independent of the color of the specimen. 6 The temperature-viscosity curve can be taken with a fair degree of accuracy while the temperature is rising or falling, as the temperature of the specimen follows the temperature of the jacket so closely. 7 The personal error which arises in determining time in- tervals with a stop watch is removed. 8 The instrument is simple, rigid and self-contained. It has no separate parts to get lost or glass parts to get broken. UNIVERSITY OF ILLINOIS-URBANA