| Temperature. | ρ Density of Water. | G Weight of 1 cub. ft. in ℔. | |
| Cent. | Fahr. | ||
| 0 | 32.0 | .999884 | 62.417 |
| 1 | 33.8 | .999941 | 62.420 |
| 2 | 35.6 | .999982 | 62.423 |
| 3 | 37.4 | 1.000004 | 62.424 |
| 4 | 39.2 | 1.000013 | 62.425 |
| 5 | 41.0 | 1.000003 | 62.424 |
| 6 | 42.8 | .999983 | 62.423 |
| 7 | 44.6 | .999946 | 62.421 |
| 8 | 46.4 | .999899 | 62.418 |
| 9 | 48.2 | .999837 | 62.414 |
| 10 | 50.0 | .999760 | 62.409 |
| 11 | 51.8 | .999668 | 62.403 |
| 12 | 53.6 | .999562 | 62.397 |
| 13 | 55.4 | .999443 | 62.389 |
| 14 | 57.2 | .999312 | 62.381 |
| 15 | 59.0 | .999173 | 62.373 |
| 16 | 60.8 | .999015 | 62.363 |
| 17 | 62.6 | .998854 | 62.353 |
| 18 | 64.4 | .998667 | 62.341 |
| 19 | 66.2 | .998473 | 62.329 |
| 20 | 68.0 | .998272 | 62.316 |
| 22 | 71.6 | .997839 | 62.289 |
| 24 | 75.2 | .997380 | 62.261 |
| 26 | 78.8 | .996879 | 62.229 |
| 28 | 82.4 | .996344 | 62.196 |
| 30 | 86 | .995778 | 62.161 |
| 35 | 95 | .99469 | 62.093 |
| 40 | 104 | .99236 | 61.947 |
| 45 | 113 | .99038 | 61.823 |
| 50 | 122 | .98821 | 61.688 |
| 55 | 131 | .98583 | 61.540 |
| 60 | 140 | .98339 | 61.387 |
| 65 | 149 | .98075 | 61.222 |
| 70 | 158 | .97795 | 61.048 |
| 75 | 167 | .97499 | 60.863 |
| 80 | 176 | .97195 | 60.674 |
| 85 | 185 | .96880 | 60.477 |
| 90 | 194 | .96557 | 60.275 |
| 100 | 212 | .95866 | 59.844 |
The weight per cubic foot has been calculated from the values of ρ, on the assumption that 1 cub. ft. of water at 39.2° Fahr. is 62.425 ℔. 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 ℔ per cub. ft., which is its density at 53° Fahr. It may be noted also that ice at 32° Fahr. contains 57.3 ℔ per cub. ft. The values of ρ 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 OO, 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 ω be the area of section of the pipe, h the height of the pressure column, p the intensity of pressure at P; then
pω = Ghω ℔,
p/G = h;
that is, h is the height due to the pressure at p. The level OO will be termed the free surface level corresponding to the pressure at P.
Relation of Pressure, Temperature, and Density of Gases
| Fig. 3. |
§ 9. Relation of Pressure, Volume, Temperature and Density in Compressible Fluids.—Certain problems on the flow of air and steam are so similar to those relating to the flow of water that they are conveniently treated together. It is necessary, therefore, to state as briefly as possible the properties of compressible fluids so far as knowledge of them is requisite in the solution of these problems. Air may be taken as a type of these fluids, and the numerical data here given will relate to air.
Relation of Pressure and Volume at Constant Temperature.—At constant temperature the product of the pressure p and volume V of a given quantity of air is a constant (Boyle’s law).