§3.3 Motion analysis of fluid parcel

3.3.1 Composition of fluid parcel motion

The particle is micelles, micellar motions were decomposited the Helmholtz. Motion of fluid particle may be subj ected to translation, rotation and deformation (including linear deformation and angular deformation).Actually, many movement of fluid was combined with motion translation, rotation and deformation (see Fig.3-10).

3.3.2 Rotation motion of fluid parcel

It is antisymmetric so its diagonal elements are zero and its off-diagonal elements are equal and opposite.Furthermore, its three independent elements can be put in correspondence with a vector.

Defining O:(u, v), A:(uA, vA)

dt:

Similarly

So

Defining

Similarly

3.3.3 Rotational flow and irrotational flow

Rotational flow is also called Vortex flow.The fluid particles of rotational flow rotate about its axis, and is independent of motion path.One of the three components (ωx, ωy, ωz)of the rotation is not zero at least.

Rotational flow or irrotational flow depends on whether fluid particles rotate about its axis, and is independent of motion path(see Fig.3-11 a).

Irrotational flow is also called Potential Flow, in which elements will translate or deform but not rotate, that is, fluid particles will not rotate about its any axes(see Fig. 3-11b).

or

The flow is irrotational flow, otherwise it is rotational flow.