Q = ∫ dp/ρ + V,
(7)
and taking dx, dy, dz in the direction of u, v, w, and
dx : dy : dz = u : v : w,
| D | ( u dx + v dy + w dz ) = | Du | dx + u | D dx | + ... = −dQ + ½ dq2, |
| dt | dt | dt |
(8)
and integrating round a closed curve
| D | ∫ (u dx + v dy + w dz) = 0, |
| dt |
(9)
and the circulation in any circuit composed of the same fluid particles is constant; and if the motion is differential irrotational and due to a velocity function, the circulation is zero round all reconcilable paths. Interpreted dynamically the normal pressure of the surrounding fluid on a tube cannot create any circulation in the tube.