ρghla = 2lT cos α,
whence
h = 2T cos α/ρga.
This expression is the same as that for the rise of a liquid in a tube, except that instead of r, the radius of the tube, we have a the distance of the plates.
Form of the Capillary Surface.—The form of the surface of a liquid acted on by gravity is easily determined if we assume that near the part considered the line of contact of the surface of the liquid with that of the solid bounding it is straight and horizontal, as it is when the solids which constrain the liquid are bounded by surfaces formed by horizontal and parallel generating lines. This will be the case, for instance, near a flat plate dipped into the liquid. If we suppose these generating lines to be normal to the plane of the paper, then all sections of the solids parallel to this plane will be equal and similar to each other, and the section of the surface of the liquid will be of the same form for all such sections.
| Fig. 7. |
Let us consider the portion of the liquid between two parallel sections distant one unit of length. Let P1, P2 (fig. 7) be two points of the surface; θ1, θ2 the inclination of the surface to the horizon at P1 and P2; y1, y2 the heights of P1 and P2 above the level of the liquid at a distance from all solid bodies. The pressure at any point of the liquid which is above this level is negative unless another fluid as, for instance, the air, presses on the upper surface, but it is only the difference of pressures with which we have to do, because two equal pressures on opposite sides of the surface produce no effect.
We may, therefore, write for the pressure at a height y
p = −ρgy,