Engler degree
Non-SI unit of conventional viscosity · quantity: a liquid's resistance to flow
The data plate on an old gear pump often calls for oil «no thicker than 8 °E at 50 °C», and a reader used to centistokes takes that line with bewilderment, because no physical meaning stands behind the number. The Engler degree is a ratio of two times: how many seconds two hundred millilitres of the liquid take to run out of a brass vessel through a calibrated orifice, and how many seconds the same charge of water takes from the same vessel. Water therefore equals one by definition, and an oil that flows eight times more slowly is given eight degrees.
The unit is built so that the instrument serves as its own standard, and that at once explains both its convenience and its misfortune: the funnel could be made in any works laboratory, but in Germany it was made after Engler, in Britain after Redwood, in America after Saybolt, and one and the same crude was given three incomparable numbers. All three moved over to centistokes only in the second half of the twentieth century, whereas the plates on pumps, gearboxes and fuel-oil plants stayed written the old way, and they still have to be converted today.
01 · Definition
The Engler degree is the ratio of the efflux time of two hundred millilitres of the liquid under test to the efflux time of the same charge of distilled water at twenty degrees Celsius, both measurements being made on one and the same instrument. Water's time is called the water value; on a sound viscometer it comes out at fifty-one seconds with a tolerance of one second.
A relation to kinematic viscosity does exist, but it is not linear, and the reason is thoroughly physical: the liquid leaves the orifice not by viscous friction alone but also by inertia, so part of the head goes into the kinetic energy of the jet. While the liquid is thick the inertial correction can be neglected and the degree converts to centistokes almost proportionally, whereas for fluid liquids the correction grows comparable with the measurement itself. For this reason the Ubbelohde formula is not applied below 1.35 °E, and the Engler funnel is not used at all for liquids thinner than five square millimetres per second.
The temperature of measurement is always stated and enters the record on equal terms with the number, since an oil's viscosity halves for every twenty degrees of heating. German practice ran tests at twenty, fifty and a hundred degrees; Soviet practice, which inherited the same instrument under the name of conventional viscosity, kept more often to fifty and eighty — and that last temperature even entered the grades of fuel oil, where the number in M-40 or M-100 comes from the viscosity at eighty degrees.
A quantity defined through its own instrument has no standard in the ordinary sense of the word: what is reproducible is not the viscosity but the pair «vessel plus orifice», calibrated against water. Hence both the requirement to check the water value before every run, and the prohibition on converting someone else's degrees when it is not known on what instrument and at what temperature they were obtained.
Heat the sample with the slider and the jet from the orifice will run faster: the stopwatch, and with it the Engler degree, answers to temperature far more sharply than one might expect. The column on the left shows how long two hundred millilitres take, and the rows on the right show how one and the same state is read by four different scales.
The solid line is the true dependence of centistokes on degrees; the dashed one is the plain proportion with the coefficient 7.31. For thick oils, to the right of the vertical, the two lines almost coincide; to the left, where the liquid flows easily, the proportion overstates the viscosity, because the jet leaves the orifice by inertia. The red mark shows the region below 1.35 °E in which the measurement is simply not held to be reliable.
02 · Conversion
Enter what the data plate says
All conventional scales are reduced to a single kinematic viscosity, so conversion between them is mechanical; its accuracy, however, is not absolute: Saybolt and Redwood seconds are tied to centistokes by formulas just as approximate as the one Ubbelohde derived for his own instrument.
The instrument's water value is placed in the fine settings of the sheet, since the efflux time depends on it directly: one second of difference in the calibration gives about two per cent in the result.
A number cannot be converted without a temperature, and that is no quibble: one and the same oil gives about twelve degrees at fifty degrees Celsius and less than three at a hundred. If the temperature is not written on a pump's data plate, fifty degrees is read by default for industrial oils and eighty for fuel oil — but it is better to find the edition of the standard the plate was drawn up under.
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03 · Orders of magnitude
logarithmic scale: from water to bitumen04 · Measuring instruments
What viscosity is measured with
A brass vessel in a water or oil bath, a conical orifice underneath and a wooden plug that is pulled at the same moment the stopwatch is started. Two hundred millilitres are collected in a measuring flask, and the instrument itself is calibrated against water before a run, since both orifice and volume drift from their certified values with time.
The American relative of the same funnel: an orifice of a different calibre, a charge of sixty millilitres, and a result called simply seconds. The number comes out about thirty times larger than Engler's, and it is still met with in oil reports in English, although ASTM long ago gave precedence to centistokes.
A glass tube with two marks between which the meniscus passes: the time of fall is multiplied by the capillary constant and gives centistokes directly, without any conventional scales. The method is described in ISO 3104 and ASTM D445, and it is what displaced the funnels, since it needs a thimbleful of sample and does not depend on whose hand holds the stopwatch.
A spindle is turned in the sample and the torque on the shaft is measured, so the time of the experiment does not depend on thickness and is the same for oil and for bitumen. The rotor can do what the funnel cannot: it sets the shear rate, and so it alone shows that an additive-treated lubricant thins under fast shear.
05 · Writing rules
A degree without a temperature means nothing
The degree sign is set closed up to the capital Latin letter, the value is separated by a space, and the temperature of measurement is always stated, because without it the number can be neither checked nor converted. The Soviet symbol for conventional viscosity is written in Cyrillic and likewise with a temperature; equating degrees to centistokes with an equals sign, however, is not permissible even in a draft: the relation between them is approximate and one-way.
The second form confuses the quantity with the instrument, since there are no degrees of viscosity — there is a ratio of times taken on a particular funnel. The third puts an equals sign where an approximation belongs, and so in a report it gives false precision. The fourth is simply impossible: below 1.35 °E the method does not work, and a number obtained for so fluid a liquid reflects not viscosity but the inertia of the jet.
06 · Neighbouring units
The nearest kin are the other conventional scales, built in exactly the same way: the efflux time of a charge through a calibrated orifice, only each country's orifice is its own. They all converge on kinematic viscosity, and that is tied to dynamic viscosity through density — and it is this pair that has a real dimension and a real standard.
water equals one
the answer straight in seconds
Redwood No. 1 second
Of the Simetrium data sheets nearby stand ISO VG and SAE oil viscosity grades, to which this sheet is the companion, poise and stokes from the CGS system, and also density in kg/m³, without which there is no going from kinematic viscosity to dynamic.
07 · Historical section
Three funnels of three countries
Carl Engler worked on refining crude and needed a number by which consignments arriving from Baku and Pennsylvania could be compared. He assembled the instrument from what stood in the laboratory, and took water as the measure, since it was to hand for any colleague and called for no tables at all.
The British expert Boverton Redwood and the American engineer George Saybolt each made his own funnel, and neither divided the time by water: they called the result plainly in seconds. The idea behind the three instruments was the same, the orifice calibres differed, and in disputes between supplier and buyer this turned into three different numbers for one tank car.
When trade became international, the incomparability of the scales grew costlier than their convenience, and the standards went over to kinematic viscosity measured by capillary. The German DIN 51560 was withdrawn, ASTM kept Saybolt seconds only as a reference conversion, and conventional viscosity under GOST 6258 held on in domestic practice for decades more.
Viscosity today is measured by capillary or by rotor, but the pumps, gearboxes and fuel-oil plants installed before the changeover go on working to their own plates. A fitter reading «no thicker than 8 °E at 50 °C» converts it into sixty square millimetres per second and then chooses the oil by its ISO VG grade — so the unit lives not in the laboratory but in the paperwork.
An instrument that is its own standard
The Engler degree has no standard in the ordinary sense and can have none, since the definition refers not to a constant of nature but to a construction: a vessel of such a volume, an orifice of such a calibre, a charge of two hundred millilitres. What is certified, therefore, is not the unit but the instrument, and it is certified against water — the one liquid whose efflux time is agreed to be known. From this follows the whole ritual side of the measurement: a fresh water value before a run, three agreeing readings, the bath temperature written down.
The weakness of such a construction showed itself exactly where its convenience was greatest. While a works compared its own consignments on its own funnel, the numbers agreed splendidly; but as soon as consignments of two countries had to be compared, it turned out that they had no common quantity — only three records, between which nothing better than an approximate conversion is possible. The capillary viscometer solved the problem by giving the measurement a dimension back: it yields square millimetres per second, and the capillary constant is verified against reference liquids rather than against its own past.
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