The physical properties of-fresh water are well known and are stated in engineers’ handbooks and in textbooks on hydraulics. One can readily find, for example, that pure water at ordinary air temperatures weighs about 62.4 pounds per cubic foot and that fresh river water weighs about 62.5. Usually there is added a table giving the weight for various temperatures.
When we consult the handbooks and hydraulic texts for similar information concerning sea water, however, we usually find nothing at all or else the bare statement that it weighs 64 pounds per cubic foot. Even the English and American books on oceanography say almost nothing about the weight of sea water.
The purpose of this article is to give the essential facts as to the weight of sea water and to show just how the weight varies with salinity and temperature. The data relative to temperature and salinity have been taken mostly from the article “Ocean and Oceanography” in the Encyclopedia Britannica, and the temperature coefficients needed in the computations have been taken from Knudsen’s Hydrographical Tables. Formula (1) was obtained by combining two formulas given in Knudsen’s tables, and (2) was taken from the tables directly. Formula (4), near the end of the paper, was derived empirically from known values of the weight of sea water of different salinities.
The weight of sea water depends principally upon its salinity, which is defined as the number of grams of dissolved salts in 1,000 grams of sea water. Thus, S=35.7 means that there are 35.7 grams of dissolved salts in each 1,000 grams of the sea water in question. In all the formulas of this article the salinity must be expressed as parts per thousand and not as percentages.
The weight of sea water depends also upon its temperature, but to a far less extent than upon salinity. And whereas the weight varies directly with salinity for a given temperature it varies in a quite complicated manner with changes in temperature. The fundamental formulas for computing the weight of sea water when the salinity and temperature are known are as follows:
Corresponding values of s0 and S are tabulated side by side in Knudsen’s tables. Hence it is not necessary to compute s0 from (1). The quantities St, At, Bt, are functions of the temperature alone and are given in Knudsen’s tables by steps of 0°.1 from —2°C to 33°C. Their actual values in terms of the temperature t (Centigrade) are:
The factor (1+ st /1000) is the specific gravity of sea water at t°C, and the number 62.424 is the weight of a cubic foot of distilled water at 4°C.
The salinity of the open seas and oceans varies from 1 to 43. The Baltic Sea has the lowest and the Red Sea the highest, the averages for these two seas being 7.21 and 39.76, respectively. The saltiest ocean is the Atlantic, having an average salinity of 36.01. The salinity of the oceans varies with the latitude, being lowest in the equatorial and polar regions and highest in the belts lying from 20° to 30° north of the equator and from 10° to 25° south of it. The salinity limits for the Atlantic are from 34.5 in the equatorial regions to 37.9 in the North Atlantic, and for the Pacific they are from 33.5 in the East Pacific equatorial belt to 36.9 in the South Pacific. For the Indian Ocean the salinity varies from 34.0 to 36.7. The average salinity for all the oceans is between 34.5 and 35.0.
The surface temperature of the oceans varies from about —2°C up to 32°.2 C (90°F), and it goes even as high as 34°.5 C (94°F) in the Red Sea. The average for all the oceans is about 17°.5 C (63°.5F).
Let us now see how the weight of sea water varies in different localities over the earth’s surface. On substituting in formulas (2) and (3) the appropriate values of temperature and salinity for the several localities named above we find that the weight per cubic foot varies from a minimum of 62.70 for the Baltic in summer to a maximum of 64.30 for the Mediterranean and Red Sea in winter. For the Atlantic Ocean the weight varies from 63.82 to 64.15, and for the Pacific it varies from 63.77 to 64.10. In the China Sea, with a salinity of 25, it drops as low as 63.50. The highest known specific gravity for the open seas and oceans is 1.031, which gives 64.36 for the weight of a cubic foot of water. In the case of the Dead Sea and Great Salt Lake, however, the water sometimes weighs as high as 75 pounds per cubic foot. The average weight for all the oceans at the average temperature of 63°.5 F is 64.0, and this is why sea water has the reputation of weighing just 64 pounds per cubic foot.
The following simple formula will give the weight of sea water correct to four figures for all salinities when the temperature is around 63°.5 F:
4. W= 62.345+0.04766S
From the foregoing discussion it is plain that in calculations involving the weight of sea water the final results should never be given to more than three significant figures unless the weight of the water is known accurately. The same remark applies to calculations involving the weight of fresh water. In either case we should state the results to three significant figures and no more.
By means of formulas (1), (2), and (3) one could compute a double-entry table giving the weight of sea water for various temperatures and salinities. There is some need for such a table, for it would at least perform an educational service by showing at a glance that sea water does not weigh exactly 64 pounds per cubic foot.