AND DENSITY RELATION OF PRESSURE TEMPERATURE
OF LIQUIDS
§ $. Units of Volume.—In practical calculations the cubic foot and gallon are largely used, and in metric countries the litre and cubic metre (= moo litres). The imperial gallon is now exclusively used in England, but the United States have retained the old English wine gallon.
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2 Journal de Al. Liouville, t. xiii. (1868) ; Memoires de l' Ae adi m'is des Sciences de l'Institut de France, t. xxiii., xxiv. (1877).
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1 cub. ft. = 6.236 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 Water.Water at 53° F. and 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. River and spring water is not sensibly denser than pure water. But average sea water weighs 64 lb 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 lb 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 woo lb per sq. in., the compression is proportional to the pressure. The 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 (V2V1)/Vl, and the ratio of the increase of pressure p2pt to the cubical compression is sensibly constant. That is,
=(p2pt)VI/(V2V1) is constant. This constant is termed the elasticity of volume. With the notation of the differential calculus,
k=dp/( ) =Vd4.
Elasticity of Volume of Liquids.
Canton. Oersted. Colladon Regnault.
and Sturm.
Water . . 45,990,000 45,900,000 42,660,000 44,090,000
Sea water 52,900,000
Mercury 705,300,000 .. 626,10x,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 Ternperature.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 p 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.
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 assumption that r cub. ft. of water at 39.2° Fahr. is 62.425 lb. For ordinary calculations in hydraulics, the density of water (which will in future be designated by the 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 Column. Free Surface Level.Suppose a small vertical 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 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 influence on the height of the column. If this condition is complied with,the height h of the column is a measure of the pressure at the point P. Let w be the area of section of the pipe, h the height of the pressure column, p the intensity of pressure at P; then
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.
End of Article: AND DENSITY RELATION OF PRESSURE 

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