Page:Elementary Text-book of Physics (Anthony, 1897).djvu/139

 CHAPTER IV.

MECHANICS OF FLUIDS.

112. Pascal's Law.—A perfect fluid may be defined as a body which offers no resistance to shearing-stress. No actual fluids are perfect. Even those which approximate that condition most nearly, offer resistance to shearing-stress, due to their viscosity. With most however, a very short time only is needed for this resistance to vanish; and all mobile fluids at rest can be dealt with as if they were perfect, in determining the conditions of equilibrium. If they are in motion, their viscosity becomes a more important factor.

As a consequence of this definition of a perfect fluid follows a most important deduction. In a fluid in equilibrium, not acted on by any outside forces except the pressure of the containing vessel, the pressure at every point and in every direction is the same. This law was first stated by Pascal, and is known as Pascal's law.

The truth of Pascal's law appears at once from what has been proved about hydrostatic stress (§ 101). For since the fluid offers no resistance to a shearing stress, the only stress within it on any surface must be perpendicular to that surface, and hence has the same value in all directions at a point. To compare the pressure at any two points we draw a line joining them, and, with it as an axis, describe a right cylinder with an infinitesimal radius, and through the two points take cross-sections normal to the axis. Then the pressures on the cylindrical surface being everywhere normal to it, have no tendency to move it in the direction of its axis, and since it is in equilibrium, the presspres on its end surfaces must be equal.