- Generally if S denotes any closed surface, fixed in the fluid, M the mass of the fluid inside it at any time t, and 0 the angle which the outward-drawn normal makes with the velocity q at that point,
**dM**/dt = rate of increase of fluid inside the surface, (I) =flux across the surface into the interior _ - f f pq cos OdS, the integral equation of continuity. - Equation (5) becomes, by a rearrangement, dK
**dmdm****dm**din dx dt +u dx + dy +Zee dz + dx (dt +u dx +v dy +w d) = o,. **Dm****dm**Dl (8), dx - dx dt + dx dt = °' ...'**Dm****dm**Dl (8), dx - dx dt + dx dt = °' ...'- Denoting the cross-section a of a filament by dS and its mass by
**dm**, the quantity wdS/**dm**is called the vorticity; this is the same at all points of a filament, and it does not change during the motion; and the vorticity is given by w cos edS/**dm**, if dS is the oblique section of which the normal makes an angle e with the filament, while the aggregate vorticity of a mass M inside a surface S is M - l fw cos edS.

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