Hydrometer degrees
Non-SI scales for liquid density · quantity: relative density at 60 °F
The oil market is arranged so that the heavy grade is the cheap one: Athabasca bitumen sells at a discount and a light Texan grade at a premium, and the whole of that difference is written into the contract as a single figure, degrees API. Their scale runs backwards to the ordinary way of things, because the denser the liquid, the fewer degrees it is given. Zero fell on a liquid heavier than water, and water itself was allotted exactly ten.
The same glass float carries two more scales, inherited from other trades: the chemist reads degrees Baumé on the stem, the tanner and the dyer read degrees Twaddell. All three speak of one and the same thing, the depth to which the instrument has sunk into the liquid, but each does so in its own numbers and over its own range, beyond which it simply says nothing.
01 · Definition
All three degrees are no more than relative density rewritten — the ratio of the density of the liquid to that of water, both taken at the same temperature of 60 °F. The instrument is the same in all three cases, a glass float with a scale on its stem, and they differ only in the formula by which that scale was marked on the glass.
A hydrometer sinks the deeper the lighter the liquid, since it displaces exactly its own weight, and the depth of immersion turns out to be proportional not to density but to its reciprocal. Hence the shape of the formulas: in degree API and in the light Baumé scale the density sits in the denominator, so the numbers grow towards light liquids, whereas Twaddell has no denominator at all — his scale is linear in density and counts from water upwards only.
The Baumé scale has two branches, heavy and light, and the instrument always states which of them is marked. Both start from water but part company thereafter: the heavy one leads to acids and alkalis, the light one to spirits and fuel. Confusing them is easier than it seems, and on a strong acid the error in choosing the branch reaches ten degrees.
The number on the scale means something only together with the temperature at which it was taken: the glass is marked for 60 °F, and a warm sample inevitably gives too low a density. In the oil trade the correction is not guessed at but taken from the ASTM D1250 tables — the reading is first brought to the reference sixty degrees, and only then are volume and money reckoned.
Move the density: the float rises or sinks, and the three scales each read its position in their own way. Every one of them has a blind zone, and where two scales still work the third already shows nothing.
The green line is degrees API: they fall as density rises. The orange one is degrees Twaddell, which rise instead. The lines cross at water, where API gives ten and Twaddell zero, and beyond that point they part in opposite directions: one scale is marked for oil, which is lighter than water, the other for acids and alkalis, which are heavier. Nobody makes an instrument with both scales on one stem, because they share too little range.
02 · Conversion
Enter one reading and the sheet gives the others
All the scales come down to one relative density at 60 °F, and so convert into each other exactly. Inaccuracy appears only where a reading was taken at a different temperature and not brought to the reference by the tables.
The modulus of the heavy Baumé branch was taken differently in different countries — 144.3, 145 or 146.3 — and the choice of modulus is put among the fine settings of this sheet: on a strong acid the difference shows in the first figure.
Fifteen and a half degrees Celsius is neither a round number nor anyone’s whim: it is exactly 60 °F, the familiar sixty degrees of the American thermometer on which the whole arithmetic of oil rests. A warm sample shows more degrees API than are really there, and on a cargo the size of a tanker that difference is already counted in money, so the reading is first brought to the reference and only then multiplied by the volume.
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03 · Orders of magnitude
logarithmic scale: from air to osmium04 · Measuring instruments
What liquid density is taken with
A float with shot in its belly and a scale on the stem: one reads the graduation that meets the surface of the liquid. A single instrument covers a narrow band of densities, which is why they are sold in sets of six to nine in a case. The method is described in ASTM D1298 and remains legal to this day when crude is accepted.
A vessel of known volume is weighed empty and full, held in a thermostat. Of the mechanical methods this is the most accurate: the fifth figure of the density is taken with confidence. The price is time — about half an hour for one sample — but it is the pycnometer by which hydrometers themselves are verified.
A bent tube is driven at its own frequency, and the denser its contents, the more slowly it swings. The instrument computes the density from the period of oscillation and brings it to 60 °F itself. A millilitre of sample is enough and the answer takes half a minute — in the laboratory such an instrument long ago displaced the float.
In a pipeline the density is needed continuously, and there a mass flow meter is fitted: it drives two loops and, from their twist, determines mass flow and density at once. The instrument gives degrees API on the spot, so the figure reaches the custody report with no sample and no man in the loop.
05 · Writing rules
A number without the scale and without the Fahrenheit reference means nothing
The degree sign goes before the letters and tight against them, while the value is separated by a space. For Baumé the branch, heavy or light, must always be stated. With degree API the temperature may be left out only because it is always the same, 60 °F; if the sample was measured at another, that is stated expressly.
The third entry confuses the quantity with its scale: density is measured in kilograms per cubic metre, whereas degrees API are a dimensionless number computed from density. The fourth mistake is the commonest on the shop floor: sulphuric acid at 66 °Bé contains about 93 % of the monohydrate, and by no means 66 %. Percentages coincide with degrees only in Brix and Plato, where the scale was designed that way.
06 · Neighbouring units
By meaning, all the scales in which density is rewritten into numbers convenient for a trade stand close together: sugar is counted in Brix, grape must in Oechsle, oil in API, and beneath them all lies one and the same dimensionless relative density.
the scale runs backwards
two scales starting at water
linear in density
Of the the Simetrium passports the closest are density in kg/m³, to which all three scales reduce, degree Brix and degree Plato with their sugar tables, barrel, in which oil is counted by volume, and barrel of oil equivalent, where heat of combustion is added to the volume.
07 · Historical section
Salt, leather and oil
Antoine Baumé marked his stem by two points: pure water gave him zero, and a solution of fifteen parts salt to eighty-five parts water gave fifteen. He divided the distance between these marks evenly, and the result was a scale the apothecaries took up at once.
The Glasgow instrument maker William Twaddell managed without a formula: he put five thousandths of density on the degree, so that nothing needs to be computed at all. Bleaching and tanning liquors are kept in a narrow band just above water, and tanners and textile men speak in degrees Twaddell to this day.
American petroleum hydrometers were graduated for decades with a modulus of 141.5, although the Baumé formula called for 140. The Bureau of Standards, on discovering the discrepancy, chose not to remake the glass but to legalise it — and so the API scale came into being.
Density has long been taken in the laboratory with an oscillating tube, and in the pipe with a mass flow meter, yet oil contracts are still written in degrees API, and the premium for a light grade is reckoned by them. The scale has outlived its instrument: the numbers are the same, but there is no float left anywhere in the chain.
A unit with neither a standard nor its zero in place
Degree API cannot itself be verified: what is verified is the densitometer, and the degree follows from the density by formula. Two quantities need checking in this chain, density and temperature, and the second matters more than the first. Warm oil is lighter, its degrees come out higher, and by the contract it is therefore dearer; so the temperature of the sample is recorded together with the reading, and the correction is taken from tables rather than worked out in the head.
The zero of this scale stands not at water but at a density of 1.076, well past it. So the formula decreed, having been devised for liquids lighter than water: its zero ended up away from any physical meaning. Heavy grades run into negative degrees, and a minus in a custody report looks odd but counts as perfectly normal.
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