Measuring the flow through a capillary tube was the first method used for determining vis cosities, and is still the most generally employed. The law governing the flow through capil laries was found experimentally by Poiseuille in a classical investi gation published in 1842. He found that the volume of liquid which passed through a capillary in unit time was (I) proportional to the pressure, (2) proportional to the fourth power of the radius and (3) inversely proportional to the length of the tube. In symbols, if Q= volume discharged in unit time, P.= pressure, R = radius and L = length of the tube : where C is a constant characteristic for each liquid, which always increases with rising temperature. Poiseuille did not deduce co efficients of viscosity, but this was done by several physicists who treated the problem mathematically by working out the conditions of flow for one of the elementary tubes described above and integrating; the equation thus obtained is known as Poi seuille's formula: mark measured by a stop watch reading to I second. The liquid is then forced up the opposite limb, the procedure reversed and the time from to m2 taken; the two times are averaged. The volumes L and R between the marks are accurately known, and from them, the times, pressures and dimensions of the capillary; the viscosity coefficients in absolute measure are calculated by Poiseuille's formula.
In another instrument, designed by Wilhelm Ostwald and called after him, which is very generally used, the pressure producing the flow is produced simply by the column of liquid itself (fig. 5). A constant volume of liquid is charged into the wide limb from a pipette and is drawn through the capillary into the bulb well above the mark A; it is then allowed to flow out and the time between the marks A and B is taken with a stop watch. This is done once and for all for a standard liquid, the viscosity no and density of which, at a convenient temperature, are accu rately known ; the time to is found as the average of several determinations.
As the same volume of liquid is always used, the effective column of liquid is always of the same height, so that the pressures pro ducing the flow are directly proportional to the densities. If there fore the time of efflux for another liquid of density pi is found to be its viscosity is, by Poiseuille's formula: As has been mentioned, and will be discussed more fully below, the viscosity of all liquids decreases with rising temperature, and measurements are therefore carried out in a thermostat, i.e., a bath of suitable liquid, the temperature of which is kept constant by a regulating device. The viscosity coefficients of a number of pure liquids are given in Table I, and those of a number of liquids of technical interest, which are not so well defined, in Table II.
at C. is almost exactly a centipoise.
A convenient alternative method of ex pressing the viscosity of a liquid is to state the ratio n lino, where no is the vis cosity of a suitably chosen standard liquid; this ratio is called the relative viscosity.
Capillary Viscometers.—A number of instruments have been designed for meas uring viscosity by means of the flow through a capillary; they all have this in common, that a constant volume, defined by suitable marks, is forced through a capillary by a known pressure. A type of historical interest is that used by Thorpe and Rodger in a famous investigation on a large number of pure organic liquids (fig. 4). CD is the capillary, the bore and ' length of which are accurately known. A definite volume of liquid is introduced into the right hand limb with a fine pipette reaching down to R; air pressure is then applied to the left hand limb, until the liquid stands at K, any excess at the same time overflowing into the trap T2. A known pressure, meas ured by a water manometer, is then applied to the right limb, and the time which the liquid takes to fall from the mark to the Viscosity and Temperature.—Two fairly typical examples of the variation of viscosity with temperature are given in fig. 6, in which the viscosity coefficients of water and of mercury are plotted against the temperatures (lower scale for water, upper for mercury). The viscosity decreases throughout the whole range, but the decrease per degree is much greater at low than at high temperature. The viscosity of water decreases by about 2.7% per degree between o° and 10°, by about 2% per degree between r o° and etc., while the decrease is much more uniform for mercury.
No general law connecting viscosity with temperature has yet been found, although for any given liquid the variation can be represented with fair accuracy by one of a number of interpola tion formulae.