| 1 cub. ft. | = 6.236 imp. gallons | = 7.481 U.S. gallons. |
| 1 imp. gallon | = 0.1605 cub. ft. | = 1.200 U.S. gallons. |
| 1 U.S. gallon | = 0.1337 cub. ft. | = 0.8333 imp. gallon. |
| 1 litre | = 0.2201 imp. gallon | = 0.2641 U.S. gallon. |
Density of Water.—Water at 53° F. and ordinary pressure contains 62.4 ℔ per cub. ft., or 10 ℔ per imperial gallon at 62° F. The litre contains one kilogram of water at 4° C. or 1000 kilograms per cubic metre. River and spring water is not sensibly denser than pure water. But average sea water weighs 64 ℔ per cub. ft. at 53° F. The weight of water per cubic unit will be denoted by G. Ice free from air weighs 57.28 ℔ per cub. ft. (Leduc).
§ 6. Compressibility of Liquids.—The most accurate experiments show that liquids are sensibly compressed by very great pressures, and that up to a pressure of 65 atmospheres, or about 1000 ℔ per sq. in., the compression is proportional to the pressure. The chief results of experiment are given in the following table. Let V1 be the volume of a liquid in cubic feet under a pressure p1 ℔ per sq. ft., and V2 its volume under a pressure p2. Then the cubical compression is (V2 − V1)/V1, and the ratio of the increase of pressure p2 − p1 to the cubical compression is sensibly constant. That is, k = (p2 − p1)V1/(V2 − V1) is constant. This constant is termed the elasticity of volume. With the notation of the differential calculus,
| k = dp / ( − | dV | ) = − V | dp | . |
| V | dV |
Elasticity of Volume of Liquids.
| Canton. | Oersted. | Colladon and Sturm. | Regnault. | |
| Water | 45,990,000 | 45,900,000 | 42,660,000 | 44,000,000 |
| Sea water | 52,900,000 | ·· | ·· | ·· |
| Mercury | 705,300,000 | ·· | 626,100,000 | 604,500,000 |
| Oil | 44,090,000 | ·· | ·· | ·· |
| Alcohol | 32,060,000 | ·· | 23,100,000 | ·· |
According to the experiments of Grassi, the compressibility of water diminishes as the temperature increases, while that of ether, alcohol and chloroform is increased.
§ 7. Change of Volume and Density of Water with Change of Temperature.—Although the change of volume of water with change of temperature is so small that it may generally be neglected in ordinary hydraulic calculations, yet it should be noted that there is a change of volume which should be allowed for in very exact calculations. The values of ρ in the following short table, which gives data enough for hydraulic purposes, are taken from Professor Everett’s System of Units.
Density of Water at Different Temperatures.