Page:Elementary Text-book of Physics (Anthony, 1897).djvu/148

134 of the air vitiates all weighings performed in it, by diminishing the true weight of the body to be weighed and of the weights employed, by an amount proportional to their volumes. The consequent error is avoided either by performing the weighings in a vacuum produced by the air-pump, or by correcting the apparent weight in air to the true weight. Knowing the specific gravity of the weights and of the body to be weighed, and the specific gravity of air, this can easily be done.

118. Motions of Fluids.—If the parts of the fluid be moving relatively to each other or to its bounding-surface, the circumstances of the motion can be determined only by making limitations which are not actually found in Nature. There thus arise certain definitions to which we assume that the fluid under consideration conforms.

The motion of a fluid is said to be uniform when each element of it has the same velocity at all points of its path. The motion is steady when, at any one point, the velocity and direction of motion of the elements successively arriving at that point remain the same for each element. If either the velocity or direction of motion change for successive elements, the motion is said to be varying. The motion is further said to be rotational or irrotational according as the elements of the fluid have or have not an angular velocity about their axes.

In all discussions of the motions of fluids a condition is supposed to hold, called the condition of continuity. It is assumed that, in any volume selected in the fluid, the change of density in that volume depends solely on the difference between the amounts of fluid flowing into and out of that volume. In an incompressible fluid, or liquid, if the influx be reckoned plus and the efflux minus, we have, letting $$Q$$ represent the amount of the liquid passing through the boundary in any one direction, $$\textstyle \sum Q = 0.$$ The results obtained in the discussion of fluid motions must all be interpreted consistently with this condition. If the motion be such that the fluid breaks up into discontinuous parts, any results obtained by hydrodynamical considerations no longer hold true.