Is Steady Flow necessarily Streamlined Flow? What about vice versa? What is the difference between the two?
What conditions should be satisfied for a flow to be streamlined?
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2 Answers
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Here are some definitions:
A streamline is a path (not necessarily constant in time) such that the tangent at each point of the streamline denotes the velocity of the particle at that point.
A trajectory is the actual path of the particle.
A streamline flow is a flow where streamlines can be defined (as opposed to a turbulent flow where this is not the case).
A steady flow is when the streamlines are constant in time. This then also means that they coincide with the trajectories, since the curves are smooth and the particles are transported along the tangent.
Thus a steady flow is always a streamline flow, but a streamline flow need not be steady.
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Is steady flow necessarily streamlined flow ?
Yes. Steady flow is defined as flow that is not a function of time. In a steady flow, the streamlines (curves that are tangent to the velocity vector field at each point) do not change over time, so the pathlines (the trajectories of ech individual particle in the flow) will be the same as the streamlines.
See the Wikipedia article on streamlines, streaklines and pathlines which says:
In steady flow (when the velocity vector-field does not change with time), the streamlines, pathlines, and streaklines coincide.
