Practical Physics is a free textbook on basic laboratory physics. See the editorial for more information....  # The Common Hydrometer

The specific gravity of a liquid may be most easily determined to within 0.1 percent by the use of the common hydrometer.

This instrument consists of a glass bulb with a cylindrical stem, loaded so that it floats in any liquid whose specific gravity lies within certain limits, with the stem vertical and partly immersed. The depth to which it requires to be immersed in order to float is defined by the condition that the weight of the liquid displaced is equal to the weight of the hydrometer. For any liquid, therefore, within the limits, there is a definite point on the stem to which the instrument will sink, depending on the specific gravity; and the stem can be graduated in such a manner that the graduation reading gives the specific gravity at once. This is generally done by a scale attached to the inside of the stem, and hence all that has to be done to determine the specific gravity of a liquid is to float in it a suitable hydrometer, and take the scale reading at the surface. The temperature correction is to be allowed for as usual

An instrument sensitive to such slight variations of density as 0.1 percent would require to have too long a stem if used for the whole range of density commonly occurring. Hydrometers are, therefore, usually obtained in sets of three or four, each suitable for one portion only of the range. The case in which they are kept contains a long cylindrical vessel, which is convenient for floating them in and also a thermometer.

The hydrometers, vessel, and thermometer should be carefully washed and dried before replacing them in the case.

The graduation of the scale is a comparatively difficult matter, as equal increments in the length of the stem immersed do nqt correspond to equal differences of density. The scales are graduated by the instrument-makers, and we require to be able to test the accuracy of the graduation.

We can do this by taking the hydrometer readings in liquids whose specific gravities are known. Distilled water would naturally be a suitable one for the purpose. The hydrometer when floating in distilled water at 15°C. should read 0.999. The specific gravity of any other suitable liquid could be determined by one of the methods already described. The following experiment, however, serves as a very instructive method of comparing the density of any liquid with that of water, and it is, therefore, suggested as a means of testing the accuracy of the hydrometer scale.

To compare the Densities of two Liquids by the Aid of the Kathetometer.

If we have a U tube (fig. 11) and fill one leg with one liquid standing up to the level P, and the other with a second up to the level Q, and if R be the common surface of the liquids in the two legs PR, QR, their densities are inversely proportional to the vertical distances between P and R, Q and R.1 These can be accurately measured by the kathetometer, and the densities thus compared. If the kathetometer be not available, the heights may be measured by scales placed behind the tubes, which are read by a telescope placed at a distance and roughly levelled for each observation. This arrangement supposes that the two liquids do not mix. The following apparatus is therefore more generally available:

A B C, D E F are two U tubes, the legs B C, D E being the shorter. These legs are connected together by a piece of india-rubber tubing C G D.

One liquid is poured into the tube A B, and then the other into the tube F E.

This, as it runs down the tube, compresses the air below it, thus increasing the pressure on the surface of the first liquid, and forcing it up the leg B A. The quantity poured into F E must not be sufficient to rise over the end D of the tube.

Now pour more of the first liquid into A B. This forces up the level of the liquid in E F, and after one or two repetitions of this operation the levels of the liquid in one tube will be at A and C, those in the other being at F and D.

The pressure at C and D, being that of the enclosed air, is the same.

The excess of the pressure at C above the atmospheric pressure is due to a column of liquid of height equal to the vertical distance between A and C, that at D is due to a column of the second liquid of height equal to the distance between F and D.

These distances can be observed by the kathetometer, and the densities of the two liquids are inversely proportional to them.

The surface of the liquids in the tubes will be curved, owing to capillary action. In measuring, either the bottom or the top of the meniscus, whichever be most convenient, may be observed, but it is necessary to take the same at each end of the column. The bottom will, if the liquid wet the tube, give the more accurate result.

It is well to hang up behind the tubes a sheet of white or grey paper, to afford a good background against which to see the liquids.

It is important that the temperature should remain the same during the experiment; for if it increase the pressure in the portion C G D increases, and the air there expands, thus forcing up the columns of liquid. We may avoid the difficulty this causes by the following method of taking the measurements :

Observe the height of A, then the height of C, and finally the height of A again.

Then, if the temperature has changed uniformly and the intervals between the successive measurements have been the same, the mean of the two observed heights of A will give its height at the time when the observation of the height of C was made, and the difference between these two, the mean of the observed heights of A and the height of C, will give the true height of the column.

If one liquid be water at a temperature, say, of 15° C, the ratio of the two heights gives us the specific gravity of the second liquid, for its temperature at the time of the observation, referred to water at 15° C.

If we wish to find the true specific gravity of the liquid at the temperature of the observation, 15° C., we must multiply the above ratio by the specific gravity of water at 15° C.

Suppose the second liquid is also at 15° C., and that its coefficient of expansion by heat does not differ greatly from that of water. Then the same ratio gives us the specific gravity of the liquid at 4° C. referred to water at 4° C., or the true specific gravity of the liquid at 4° C. without any correction.

Experiment. - Determine the specific gravity of the given liquid by means of the hydrometer, testing the accuracy of the results.

Enter results thus: - 1 See below, page 152.

Last Update: 2011-03-27