The velocity would be infinite at radius 0, if the current could be conceived to extend to the axis. Now, if the motion is steady,
H = p1/G + v12/2g = p2/G + v22/2g;
= p2/G + r12 + v12 / r222g;
(p2 − p1) / G = v12 (1 − r12/r22) / 2g;
(5)
p2/G = H − r12v12 / r222g.
(6)
Hence the pressure increases from the interior outwards, in a way indicated by the pressure columns in fig. 36, the curve through the free surfaces of the pressure columns being, in a radial section, the quasi-hyperbola of the form xy2 = c3. This curve is asymptotic to a horizontal line, H ft. above the line from which the pressures are measured, and to the axis of the current.
| Fig. 36. |
Free Circular Vortex.—A free circular vortex is a revolving mass of water, in which the stream lines are concentric circles, and in which the total head for each stream line is the same. Hence, if by any slow radial motion portions of the water strayed from one stream line to another, they would take freely the velocities proper to their new positions under the action of the existing fluid pressures only.