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RELATION OF PRESSURE, DENSITY, AND

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Originally appearing in Volume V14, Page 36 of the 1911 Encyclopedia Britannica.
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RELATION OF PRESSURE, See also:

DENSITY, AND TEMPERATURE OF LIQUIDS § $. See also:Units of See also:Volume.—In See also:practical calculations the cubic See also:foot and See also:gallon are largely used, and in metric countries the litre and cubic See also:metre (= moo litres). The imperial gallon is now exclusively used in See also:England, but the See also:United States have retained the old See also:English See also:wine gallon. ea_ 2 See also:Journal de Al. Liouville, t. xiii. (1868) ; Memoires de l' Ae adi m'is See also:des Sciences de l'Institut de See also:France, t. See also:xxiii., See also:xxiv. (1877). y c io/ iii~a iaasaZe0 e'/ 6 a. 1 cub. ft. = 6.236 See also:imp. gallons = 7.481 U.S. gallons. I imp. gallon = 0.1605 cub. ft. = I •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 See also:

Water.-Water at 53° F. and See also:ordinary pressure contains 62.4 lb per cub. ft., or to lb per imperial gallon at 62° F. The litre contains one kilogram of water at 4° C. or woo kilograms per cubic metre. See also:River and See also:spring water is not sensibly denser than pure water. But See also:average See also:sea water weighs 64 lb per cub. ft. at 53° F. The See also:weight of water per cubic unit will be denoted by G. See also:Ice See also:free from See also:air weighs 57.28 lb per cub. ft. (Leduc). § 6. Compressibility of Liquids.-The most accurate experiments show that liquids are sensibly compressed by very See also:great pressures, and that up to a pressure of 65 atmospheres, or about woo lb per sq. in., the See also:compression is proportional to the pressure.

The See also:

chief results of experiment are given in the following table. Let V, be the volume of a liquid in cubic feet under a pressure pt lb per sq. ft., and V2 its volume /~ ~under a pressure p2. Then the cubical compression is (V2-V1)/Vl, and the ratio of the increase of pressure p2-pt to the cubical compression is sensibly See also:constant. That is, =(p2-pt)VI/(V2-V1) is constant. This constant is termed the See also:elasticity of volume. With the notation of the See also:differential calculus, k=dp/(- ) =-Vd4. Elasticity of Volume of Liquids. See also:Canton. Oersted. Colladon See also:Regnault. and See also:Sturm. Water .

. 45,990,000 45,900,000 42,660,000 44,090,000 Sea water 52,900,000 See also:

Mercury 705,300,000 .. 626,10x,000 604,500,000 Oil . 44,090,000 See also: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 See also:ether, alcohol and See also:chloroform is increased. § 7. See also:Change of Volume and Density of Water with Change of Ternperature.-Although the change of volume of water with change of temperature is so small that it may generally be neglected in ordinary See also: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 p in the following See also:short table, which gives data enough for hydraulic purposes, are taken from See also:Professor See also:Everett's See also:System of Units. Density of Water at Different Temperatures. Temperature. P G Temperature. P G Density of weight of Density of weight of Cent. Fahr.

Cent. Fahr. water- ' cub. ft. water. I cub. ft. in m. in tD. 0 32'0 •999884 62.417 20 68•o .998272 62'316 1 33v8 .999941 62.420 22 71'6 '997839 62.289 2 35'6 .999982 62.423 24 75'2 997380 62.261 3 37'4 1.000004 62.424 26 78.8 •996879 62.229 4 39.2 I•0000I3 62.425 28 82.4 996344 62.196 5 41'0 1'000003 62.424 30 86 .995778 62.161 6 42'8 '999983 62.423 35 95 99469 62.093 7 44'6 .999946 62.421 40 104 .99236 61'947 8 46.4 .999899 62.418 45 I13 .99038 61.823 9 48.2 '999837 62.414 50 122 .98821 61.688 10 50.0 .999760 62.409 55 131 .98583 61.540 II 51.8 .999668 62.403 60 140 .98339 61.387 12 53'6 .999562 62.397 65 149 .98075 61.222 13 55.4 '999443 62.389 70 158 97795 61.048 14 57.2 .999312 62.381 75 167 97499 60.863 15 59.0 .999173 62.373 8o 176 .97195 60.674 16 60.8 .999015 62.363 85 185 .96880 60.477 17 62.6 .998854 62.353 90 194 '96557 60'275 18 64.4 .998667 62.341 100 212 .95866 59'844 19 66.2 •998473 62.329 The weight per cubic foot has been calculated from the values of p, on the See also:

assumption that r cub. ft. of water at 39.2° Fahr. is 62.425 lb. For ordinary calculations in See also:hydraulics, the density of water (which will in future be designated by the See also:symbol G) will be taken at 62.4 lb per cub. ft., which is its density at 53° Fahr. It may be noted also that ice at 32° Fahr. contains 57.3 lb per cub. ft. The values of p are the densities in grammes per cubic centimetre. § 8.

Pressure See also:

Column. Free See also:Surface Level.-Suppose a small See also:vertical See also:pipe introduced into a liquid at any point P (fig. 3). Then the liquid will rise in the pipe to a level 00, such that the pressure due to the column in the pipe exactly balances the pressure on its mouth. If the fluid is in See also:motion the mouth of the pipe must be supposed accurately parallel to the direction of motion, or the impact of the liquid at the mouth of the pipe will have an See also:influence on the height of the column. If this See also:condition is complied with,the height h of the column is a measure of the pressure at the point P. Let w be the See also:area of See also:section of the pipe, h the height of the pressure column, p the intensity of pressure at P; then See also:pro = Ghwlb, p/G=h; that is, h is the height due to the pressure at p. The level 00 will be termed the free surface level corresponding to the pressure at P.

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