Two-dimensional flow

Fluid motion can be said to be a two-dimensional flow when the flow velocity at every point is parallel to a fixed plane. The velocity at any point on a given normal to that fixed plane should be constant.

Considering a two dimensional flow in the ${\displaystyle X-Y}$ plane, the flow velocity at any point ${\displaystyle (x,y,z)}$ at time ${\displaystyle t}$ can be expressed as –

Considering a two dimensional flow in the ${\displaystyle r-\theta }$ plane, the flow velocity at a point ${\displaystyle (r,\theta ,z)}$ at a time ${\displaystyle t}$ can be expressed as –

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