According to J. Clerk Maxwell, the value of μ for air at θ° Fahr. in pounds, when the velocities are expressed in feet per second, is
μ = 0.000 000 025 6 (461° + θ);
that is, the coefficient of viscosity is proportional to the absolute temperature and independent of the pressure.
The value of μ for water at 77° Fahr. is, according to H. von Helmholtz and G. Piotrowski,
μ = 0.000 018 8,
the units being the same as before. For water μ decreases rapidly with increase of temperature.
| Fig. 2. |
§ 4. When a fluid flows in a very regular manner, as for instance when It flows in a capillary tube, the velocities vary gradually at any moment from one point of the fluid to a neighbouring point. The layer adjacent to the sides of the tube adheres to it and is at rest. The layers more interior than this slide on each other. But the resistance developed by these regular movements is very small. If in large pipes and open channels there were a similar regularity of movement, the neighbouring filaments would acquire, especially near the sides, very great relative velocities. V. J. Boussinesq has shown that the central filament in a semicircular canal of 1 metre radius, and inclined at a slope of only 0.0001, would have a velocity of 187 metres per second,[2] the layer next the boundary remaining at rest. But before such a difference of velocity can arise, the motion of the fluid becomes much more complicated. Volumes of fluid are detached continually from the boundaries, and, revolving, form eddies traversing the fluid in all directions, and sliding with finite relative velocities against those surrounding them. These slidings develop resistances incomparably greater than the viscous resistance due to movements varying continuously from point to point. The movements which produce the phenomena commonly ascribed to fluid friction must be regarded as rapidly or even suddenly varying from one point to another. The internal resistances to the motion of the fluid do not depend merely on the general velocities of translation at different points of the fluid (or what Boussinesq terms the mean local velocities), but rather on the intensity at each point of the eddying agitation. The problems of hydraulics are therefore much more complicated than problems in which a regular motion of the fluid is assumed, hindered by the viscosity of the fluid.
Relation of Pressure, Density, and Temperature of Liquids
§ 5. Units of Volume.—In practical calculations the cubic foot and gallon are largely used, and in metric countries the litre and cubic metre (= 1000 litres). The imperial gallon is now exclusively used in England, but the United States have retained the old English wine gallon.